The  moon.     From  a  photograph  taken  at  the  Lick  Observatory. 

[Frontispiece, 


THE   UNIVERSITY  SERIES 


A     Short     History 


of 


Astronomy 


BY    ARTHUR    BERRY,    M.A. 

FELLOW   AND  ASSISTANT   TUTOR  OF   KING'S   COLLEGE,   CAMBRIDGE; 
FELLOW  OF  UNIVERSITY   COLLEGE,   LONDON 


Wagner.  Verzeiht !  es  ist  ein  gross  Ergetzen 
Sich  in  den  Geist  der  Zeiten  zu  versetzen, 
Zu  schauen  wie  vor  uns  ein  weiser  Mann  gedacht, 
Und  wie  wir's  dann  zuletzt  so  herrlich  weit  gebracht. 

Faust.  O  ja,  bis  an  die  Sterne  weit ! 

GOETHE'S  Faust. 


NEW  YORK 

CHARLES    SCRIBNER'S   SONS 
1910 


PREFACE. 


I  HAVE  tried  to  give  in  this  book  an  outline  of  the  history 
of  astronomy  from  the  earliest  historical  times  to  the  present 
day,  and  to  present  it  in  a  form  which  shall  be  intelligible 
to  a  reader  who  has  no  special  knowledge  of  either  astronomy 
or  mathematics,  and  has  only  an  ordinary  educated  person's 
power  of  following  scientific  reasoning. 

In  order  to  accomplish  my  object  within  the  limits  of 
one  small  volume  it  has  been  necessary  to  pay  the  strictest 
attention  to  compression ;  this  has  been  effected  to  some 
extent  by  the  omission  of  all  but  the  scantiest  treatment 
of  several  branches  of  the  subject  which  would  figure 
prominently  in  a  book  written  on  a  different  plan  or  on 
a  different  scale.  I  have  deliberately  abstained  from  giving 
any  connected  account  of  the  astronomy  of  the  Egyptians, 
Chaldaeans,  Chinese,  and  others  to  whom  the  early  develop- 
ment of  astronomy  is  usually  attributed.  On  the  one 
hand,  it  does  not  appear  to  me  possible  to  form  an  in- 
dependent opinion  on  the  subject  without  a  first-hand 
knowledge  of  the  documents  and  inscriptions  from  which 
our  information  is  derived ;  and  on  the  other,  the  various 
Oriental  scholars  who  have  this  knowledge  still  differ  so 
widely  from  one  another  in  the  interpretations  that  they 
give  that  it  appears  premature  to  embody  their  results  in 


300336 


vi  Preface 

the  dogmatic  form  of  a  text-book.  It  has  also  seemed 
advisable  to  lighten  the  book  by  omitting — except  in  a  very 
few  simple  and  important  cases — all  accounts  of  astro- 
nomical instruments  ;  I  do  not  remember  ever  to  have 
derived  any  pleasure  or  profit  from  a  written  description 
of  a  scientific  instrument  before  seeing  the  instrument 
itself,  or  one  very  similar  to  it,  and  I  .  have  abstained 
from  attempting  to  give  to  my  readers  what  I  have  never 
succeeded  in  obtaining  myself.  The  aim  of  the  book 
has  also  necessitated  the  omission  of  a  number  of  im- 
portant astronomical  discoveries,  which  find  their  natural 
expression  in  the  technical  language  of  mathematics.  I 
have  on  this  account  only  been  able  to  describe  in  the 
briefest  and  most  general  way  the  wonderful  and  beautiful 
superstructure  which  several  generations  of  mathematicians 
have  erected  on  the  foundations  laid  by  Newton.  For 
the  same  reason  I  have  been  compelled  occasionally 
to  occupy  a  good  deal  of  space  in  stating  in  ordinary 
English  what  might  have  been  expressed  much  more 
briefly,  as  well  as  more  clearly,  by  an  algebraical  formula  : 
for  the  benefit  of  such  mathematicians  as  may  happen  to 
read  the  book  I  have  added  a  few  mathematical  footnotes  ; 
otherwise  I  have  tried  to  abstain  scrupulously  from  the 
use  of  any  mathematics  beyond  simple  arithmetic  and  a 
few  technical  terms  which  are  explained  in  the  text.  A 
good  deal  of  space  has  also  been  saved  by  the  total 
omission  of,  or  the  briefest  possible  reference  to,  a  very 
large  number  of  astronomical  facts  which  do  not  bear  on 
any  well-established  general  theory ;  and  for  similar  reasons 
I  have  generally  abstained  from  noticing  speculative 
theories  which  have  not  yet  been  established  or  refuted. 
In  particular,  for  these  and  for  other  reasons  (stated  more 
fully  at  the  beginning  of  chapter  xni.),  I  have  dealt  in  the 
briefest  possible  way  with  the  immense  mass  of  observations 


Preface  vii 

which  modern  astronomy  has  accumulated ;  it  would,    for 
example,  have  been  easy  to  have  filled  one  or  more  volumes  % 
with  an  account  of  observations  of  sun-spots  made  during 
the  last  half-century,  and  of  theories  based  on  them,  but 
I  have  in  fact  only  given  a  page  or  two  to  the  subject. 

I  have  given  short  biographical  sketches  of  leading  astro- 
nomers (other  than  living  ones),  whenever  the  material 
existed,  and  have  attempted  in  this  way  to  make  their 
personalities  and  surroundings  tolerably  vivid ;  but  I 
have  tried  to  resist  the  temptation  of  filling  up  space 
with  merely  picturesque  details  having  no  real  bearing  on 
scientific  progress.  The  trial  of  Kepler's  mother  for  witch- 
craft is  probably  quite  as  interesting  as  that  of  Galilei 
before  the  Inquisition,  but  I  have  entirely  omitted  the  first 
and  given  a  good  deal  of  space  to  the  second,  because, 
while  the  former  appeared  to  be  chiefly  of  curious  interest, 
the  latter  appeared  to  me  to  be  not  merely  a  striking  inci- 
dent in  the  life  of  a  great  astronomer,  but  a  part  of  the 
history  of  astronomical  thought.  I  have  also  inserted  a 
large  number  of  dates,  as  they  occupy  very  little  space,  and 
may  be  found  useful  by  some  readers,  while  they  can  be 
ignored  with  great  ease  by  others;  to  facilitate  reference 
the  dates  of  birth  and  death  (when  known)  of  every 
astronomer  of  note  mentioned  in  the  book  (other  than 
living  ones)  have  been  put  into  the  Index  of  Names. 

I  have  not  scrupled  to  give  a  good  deal  of  space  to 
descriptions  of  such  obsolete  theories  as  appeared  to  me  to 
form  an  integral  part  of  astronomical  progress.  One  of  the 
reasons  why  the  history  of  a  science  is  worth  studying  is 
that  it  sheds  light  on  the  processes  whereby  a  scientific 
theory  is  formed  in  order  to  account  for  certain  facts, 
and  then  undergoes  successive  modifications  as  new  facts 
are  gradually  brought  to  bear  on  it,  and  is  perhaps 
finally  abandoned  when  its  discrepancies  with  facts  can 


viii  Preface 

no  longer  be  explained  or  concealed.  For  example,  no 
modern  astronomer  as  such  need  be  concerned  with 
the  Greek  scheme  of  epicycles,  but  the  history  of  its 
invention,  of  its  gradual  perfection  as  fresh  observations 
were  obtained,  of  its  subsequent  failure  to  stand  more 
stringent  tests,  and  of  its  final  abandonment  in  favour  of 
a  more  satisfactory  theory,  is,  I  think,  a  valuable  and 
interesting  object-lesson  in  scientific  method.  I  have  at 
any  rate  written  this  book  with  that  conviction,  and  have 
decided  very  largely  from  that  point  of  view  what  to  omit 
and  what  to  include. 

The  book  makes  no  claim  to  be  an  original  contribution 
to  the  subject ;  it  is  written  largely  from  second-hand 
sources,  of  which,  however,  many  are  not  very  accessible  to 
the  general  reader.  Particulars  of  the  authorities  which 
have  been  used  are  given  in  an  appendix. 

It  remains  gratefully  to  acknowledge  the  help  that  I  have 
received  in  my  work.  Mr.  W.  W.  Rouse  Ball,  Tutor  of 
Trinity  College,  whose  great  knowledge  of  the  history  of 
mathematics — a  subject  very  closely  connected  with  astro- 
nomy— has  made  his  criticisms  of  special  value,  has  been 
kind  enough  to  read  the  proofs,  and  has  thereby  saved  me 
from  several  errors ;  he  has  also  given  me  valuable  infor- 
mation with  regard  to  portraits  of  astronomers.  Miss  H. 
M.  Johnson  has  undertaken  the  laborious  and  tedious  task 
of  reading  the  whole  book  in  manuscript  as  well  as  in 
proof,  and  of  verifying  the  cross-references.  Miss  F. 
Hardcastle,  of  Girton  College,  has  also  read  the  proofs, 
and  verified  most  of  the  numerical  calculations,  as  well  as 
the  cross-references.  To  both  I  am  indebted  for  the 
detection  of  a  large  number  of  obscurities  in  expression, 
as  well  as  of  clerical  and  other  errors  and  of  misprints. 
Miss  Johnson  has  also  saved  me  much  time  by  making  the 
Index  of  Names,  and  Miss  Hardcastle  has  rendered  me 


Preface  ix 

a  further  service  of  great  value  by  drawing  a  consider- 
able number  of  the  diagrams.  I  am  also  indebted  to 
Mr.  C.  E.  Inglis,  of  this  College,  for  fig  81  ;  and  I  have 
to  thank  Mr.  W.  H.  Wesley,  of  the  Royal  Astronomical 
Society,  for  various  references  to  the  literature  of  the 
subject,  and  in  particular  for  help  in  obtaining  access  to 
various  illustrations. 

I  am  further  indebted  to  the  following  bodies  and 
individual  astronomers  for  permission  to  reproduce  photo- 
graphs and  drawings,  and  in  some  cases  also  for  the  gift 
of  copies  of  the  originals  :  the  Council  of  the  Royal  Society, 
the  Council  of  the  Royal  Astronomical  Society,  the  Director 
of  the  Lick  Observatory,  the  Director  of  the  Institute 
Geographico-Militare  of  Florence,  Professor  Barnard, 
Major  Darwin,  Dr.  Gill,  M.  Janssen,  M.  Loewy,  Mr.  E. 
W.  Maunder,  Mr.  H.  Pain,  Professor  E.  C.  Pickering, 
Dr.  Schuster,  Dr.  Max  Wolf. 

ARTHUR   BERRY. 

KING'S  COLLEGE,  CAMBRIDGE 


CONTENTS. 


PAGE 

PREFACE  v 


CHAPTER   I. 

PRIMITIVE  ASTRONOMY,  §§  1-18 1-20 

§  I.    Scope  of  astronomy      ...         ...         .         I 

§§  2-5.  First  notions  :  the  motion  of  the  sun  :  the  motion 
and  phases  of  the  moon  :  daily  motion  of  the 
stars  .  .  . I 

§  6.  Progress  due  to  early  civilised  peoples  :  Egyptians, 

Chinese,  Indians,  and  Chaldaeans  ...  3 

§  7.  The  celestial  sphere  :  its  scientific  value  :  apparent  dis- 
tance between  the  stars :  the  measurement  of 
•angles  . 4 

§§  8-9.  The  rotation  of  the  celestial  sphere :  the  North  and 
South  poles :  the  daily  motion  :  the  celestial 
equator  :  circumpolar  stars 7 

§§  IO-H.  The  annual  motion  of  the  sun:  great  circles: 
the  ecliptic  and  its  obliquity :  the  equinoxes  and 
equinoctial  points  :  the  solstices  and  solstitial 
points 8 

§§  12-13.  The  constellations  :  the  zodiac,  signs  of  the  zodiac, 
and  zodiacal  constellations  :  the  first  point  of 
Aries  (T),  and  ihe  first  point  of  Libra  (^)  .  12 

§  14.  The  five  planets :  direct  and  retrograde  motions : 

stationary  points 14 

§  15.  The  order  of  nearness  of  the  planets:  occultations  : 

superior  and  inferior  planets  .  .  .  1 5 


xii  Contents 

PAGE 
§  1 6.     Measurement  of  time  :  the  day  and  its  division  into 

hours  :  the  lunar  month  :  the  year  :  the  week    .       17 

§  17.     Eclipses:  the  saros 19 

§  18,    The  rise  of  Astrology 2O 

• 

CHAPTER   II. 

GREEK  ASTRONOMY  (FROM  ABOUT    600  B.C.    TO  ABOUT 

400  A.D.),  §§  19-54   .        .       .        .        .       .        .     21-75 

§§  19-20.  Astronomy  up  to  the  time  of  Aristotle.  The 
Greek  calendar :  full  and  empty  months : 
the  octaeteris  :  Meton's  cycle  .  .  .  .21 

§21.  The  Roman  calendar:  introduction  of  the 

Julian  Calendar 22 

§  22.  The  Gregorian  Calendar 23 

§  23.  Early  Greek  speculative  astronomy :  Thales 
and  Pythagoras :  the  spherical  form  of  the 
earth:  the  celestial  spheres:  the  music  of 
the  spheres 24 

§  24.  Philolaus  and  other  Pythagoreans  :  early  be- 

lievers in  the  motion  of  the  earth :  Arist- 
archus  and  Seleucus  ,  .  .  .  .25 

§  25.  Plato :  uniform  circular  and  spherical  motions  .      26 

§  26.  Eudoxus :  representation  of  the  celestial 

motions  by  combinations  of  spheres :  de- 
scription of  the  constellations.  Callippus  .  27 

§§  27~3°-  Aristotle :  his  spheres  :  the  phases  of  the  moon  : 
proofs  that  the  earth  is  spherical :  his 
arguments  against  the  motion  of  the  earth  : 
relative  distances  of  the  celestial  bodies: 
other  speculations :  estimate  of  his  astro- 
nomical work  .  ''«•'•'.  Y  .  .  29 

§§  31-2.  The  early  Alexandrine  school :  its  rise  :  Arist- 
archus  :  his  estimates  of  the  distances  of  the 
sun  and  moon.  Observations  by  Timocharis 
and  Aristyllus  .  .  ..•'.'  .  .  •  34 

§§  33~4-  Development  of  spherics  :  the  Phenomena  of 
Euclid',  the  horizon,  the  zenith,  poles  of  a 
great  circle,  verticals,  declination  circles,  the 
meridian,  celestial  latitude  and  longitude, 
right  ascension  and  declination.  Sun-dials  .  36 


Contents  xiii 

PAGE 

§  35.  The  division  of  the  surface  of  the  earth  into 

zones 37 

§  36.  Eratosthenes :  his  measurement  of  the  earth : 

and  of  the  obliquity  of  the  ecliptic  .  .  39 

§  37.  Hipparchni :  his  life  and  chief  contributions  to 
astronomy.  Apollonius's  representation  of 
the  celestial  motions  by  means  of  circles. 
General  account  of  the  theory  of  eccentrics 
and  epicycles 40 

§§  38-9'  Hipparchus's  representation  of  the  motion  of 
the  sun,  by  means  of  an  eccentric:  apogee, 
perigee,  line  of  apses,  eccentricity  :  equation  of 
the  centre  :  the  epicycle  and  the  deferent  .  41 

§  40.  Theory  of  the  moon  :  lunation  or  synodic  month 

and  sidereal  month  :  motion  of  the  moon's 
nodes  and  apses :  draconitic  month  and 
anomalistic  month ....  .47 

§  41.  Observations  of  planets  :  eclipse  method  of  con- 

necting the  distances  of  the  sun  and  moon  : 
estimate  of  their  distances  ....  49 

§  42.  His  star  catalogue.  Discovery  of  the  precession 
of  the  equinoxes :  the  tropical  year  and  the 
sidereal  year 51 

§  43.  Eclipses  of  the  sun  and  moon :  conjunction 
and  opposition:  partial,  total,  and  annular 
eclipses :  parallax 56 

§  44.  Delambre's  estimate  of  Hipparchus  6l 

§  45.  The  slow  progress  of  astronomy  after  the  time  of  Hip- 
parchus :  Pliny's  proof  that  the  earth  is  round  : 
new  measurements  of  the  earth  by  Posidonius  .  61 

§  46.  Ptolemy.  The  Almagest  and  the  Optics  :  theory  of 

refraction 62 

§  47.  Account  of  the  Almagest :  Ptolemy's  postulates : 

arguments  against  the  motion  of  the  earth  .  63 

§  48.  The  theory  of  the  moon  :  evection  and  prosneusis      65 

§  49.  The  astrolabe.  Parallax,  and  distances  of  the 

sun  and  moon 67 

§  5°-  The  star  catalogue  :  precession  .          ...      68 

§51.  Theory  of  the  planets :  the  equant      ...       69 

§  52-  Estimate  of  Ptolemy    .         .         .  .         -73 

§  53.     The  decay  of  ancient  astronomy  :  Theon  ai.d  Hypatia       73 

§  54-     Summary  and  estimate  of  Greek  astronomy      .        .       74 


xiv  Contents 

CHAPTER    III. 


PAGE 


THE    MIDDLE    AGES   (FROM  ABOUT   600  A.D.  TO  ABOUT 

1500  A.D.),  §§  55-69     •        •        -  76-91 

§  55.  The  slow  development  of  astronomy  during  this 

period 76 

§  56.  The  East.  The  formation  of  an  astronomical  school 
at  the  court  of  the  Caliphs :  revival  of 
astrology :  translations  from  the  Greek  by 
Honein  ben  Ishak,  Ishak  ben  Honem,  Tabit 
ben  Korra,  and  others 76 

§§  57-8-  The  Bagdad  observatory.  Measurement  of  the 
earth.  Corrections  of  the  astronomical  data 
of  the  Greeks  :  trepidation  ....  78 

§  59.  Albategnius  :  discovery  of  the  motion  of  the 

sun's  apogee 79 

§  60.  Abul  Wafa  :  supposed  discovery  of  the  variation 
of  the  moon.  Ibn  Yunos :  the  Hakemite 
Tables 79 

§  6l.  Development  of  astronomy  in  the  Mahometan 
dominions  in  Morocco  and  Spain  :  Arzacheli 
the  Toletan  Tables 80 

§  62.  Nassir  Eddin  and  his  school :  Ilkhanic  Tables  : 

more  accurate  value  of  precession  .  .  81 

§  63.  Tartar  astronomy :  Ulugh  Begh  :  his  star  cata- 
logue   82 

§  64.  Estimate  of  oriental  astronomy  of  this  period  : 

Arabic  numerals :  survivals  of  Arabic  names 
of  stars  and  astronomical  terms  :  nadir  .  82 

§65.  The  West.  General  stagnation  after  the  fall  of  the 
Roman  Empire  :  Bede.  Revival  of  learning 
at  the  court  of  Charlemagne  :  Alcuin  .  .  83 

§  66.  Influence  of  Mahometan  learning :  Gerbert : 

translations  from  the  Arabic  :  Plato  ofTivoli, 
Athelard  of  Bath,  Gherardo  of  Cremona. 
Alfonso  X.  and  his  school :  the  Alfonsine 
Tables  and  the  Libros  del  Saber  .  .  '.84 

§67.  The  schoolmen  of  the  thirteenth  century, 

Albertus  Magnus,  Cecco  d"Ascoli,  Roger 
Bacon.  Sacrobosco 's  Sphacra  Mundi  ,  .  85 


Contents  xv 

PAGE 

§  68.  Purbach  and  Regiomontanus:  influence  of  the 

original  Greek  authors :  the  Niirnberg  school : 
Walther  :  employment  of  printing  :  conflict 
between  the  views  of  Aristotle  and  of 
Ptolemy  :  the  celestial  spheres  of  the  Middle 
Ages  :  the  firmament. and  theprimum  mobile  86 

§  69.  Lionardo  da  Vinci:  earthshine.  Fracastor  and 

Apian  :  observations  of  comets.  Nonius. 
Fernet s  measurement  of  the  earth  .  .  90 


CHAPTER   IV. 

COPPERNICUS  (FROM  1473  A.D.  TO  1543  A.D.),  §§  70-92  .  92-124 

§  70.     The  Revival  of  Learning 92 

§§  71-4.  Life  of  Coppernicus  :  growth  of  his  ideas:  publi- 
cation of  the  Commentariolus :  Rheticus  and  the 
Prima  Narratio  :  publication  of  the  De  Revo- 

lutionibus '  93 

§  75.     The   central   idea    in   the   work    of    Coppernicus  : 

relation  to  earlier  writers 99 

§§  76-9.  The  De  Revolutionibus.  The  first  book  :  the 
postulates  :  the  principle  of  relative  motion, 
with  applications  to  the  apparent  annual 
motion  of  the  sun,  and  to  the  daily  motion 

of  the  celestial  sphere 100 

§  80.  The   two  motions   of  the   earth  :    answers    to 

objections 105 

§  81.  The  motion  of  the  planets 106 

§  82.  The  seasons 108 

§  83.  End  of  first  book.     The  second  book  :  decrease 

in  the   obliquity  of  the   ecliptic  :    the   star 

catalogue HO 

§  84.  The  third  book :  precession I IO 

§  85.  The  third  book  :  the  annual  motion  of  the  earth  : 

aphelion  and  perihelion.     The  fourth    book  : 
theory  of  the  moon  :  distances  of  the  sun 

and  moon  :  eclipses ill 

§§  86-7.       The  fifth  and  sixth  booxs  :  theory  of  the  planets  : 

synodic  and  sidereal  periods  .          .         .          .112 
§88.  Explanation  of  the  stationary  points  .         .         .     118 


xvi  Contents 

PAGE 

§§  89-90.     Detailed  theory  of  the  planets  :  defects  of  the 

theory 121 

§91.     Coppernicus's  use  of  epicycles 122 

§  92.     A  difficulty  in  his  system  .         .        .        .        »        (  123 


CHAPTER    V. 

THE  RECEPTION  OF  THE  COPPERNICAN  THEORY  AND  THE 
PROGRESS  OF  OBSERVATION  (FROM  ABOUT   1543  A.D. 

TO  ABOUT    l6oi    A.D.),    §§93~II2.  .  .  .     I2J-I44 

§§  93~4-     The   first   reception   of  the   De  Revolutionibus : 

Reinhold:  the  Prussian  Tables  .  .  .  .  .125 
§  95.  Coppernicanism  in  England  :  Field,  Recorde,  Digges  127 
§  96.  Difficulties  in  the  Coppernican  system  :  the  need  for 

progress  in  dynamics  and  for  fresh  observations     127 
§§  97~8.     The  Cassel  Observatory  :  the  Landgrave  William 
IV.)  Rothrnann,  and  Burgi :  the  star  catalogue : 
Biirgi's  invention  of  the  pendulum  clock     .         .     128 

§  99.     Tycho  Brahe  :  his  early  life 130 

§100.          The  new  star  of  1572  :  travels  in  Germany         .     131 
§§  IOI-2.     His  establishment   in   Hveen  :   Uraniborg  and 

Stjerneborg  :  life  and  work  in  Hveen  .  .132 
§  103.  The  comet  of  1577,  and  others  .  .  .  .135 
§  104.  Books  on  the  new  star  and  on  the  comet  of  1577  136 

§  105.  Tycho's    system    of    the  world :    quarrel  with 

Reymers  Bar 136 

§  106.  Last  years  at  Hveen  :  breach  with  the  King      .     138 

§  107.  Publication    of    the    Astronomiae    Instauratae 

Mechanica  and  of  the  star  catalogue :    in- 
vitation from  the  Emperor   .         .        .        .^39 

§  108.  Life  at  Benatek  :  co-operation  of  Kepler  :  death     140 

§109.  Fate  of  Tycho's  instruments  and  observations    .     141 

§  1 10.  Estimate  of  Tycho's  work  :  the  accuracy  of  his 

observations :  improvements  in  the  art  of 
observing      .         .         .         .         .         .         .     141 

§  III.  Improved     values    of    astronomical    constants. 

Theory  of  the  moon  :    the  variation  and  the 
annual  equation         .         .         .         .        ,         143 

§112.  The   star   catalogue:   rejection  of  trepidation: 

unfinished  work  on  the  planets  .        ,         .     144 


Contents  xvii 

CHAPTER  VI. 

PAGE 

GALILEI  (FROM  1564  A.D.  TO  1642  A.D.),  §§  113-134     .     145-178 

§113.     Early  life 145 

§  114.     The  pendulum 146 

§  115.     Diversion  from  medicine  to  mathematics:  his  first 

book .        .         .     146 

§  116.     Professorship    at    Pisa:    experiments    on    falling 
bodies:     protests    against    the     principle     of 

authority 147 

§  117.     Professorship  at  Padua:   adoption  of Coppernican 

views 148 

§  118.  The  telescopic  discoveries.  Invention  of  the  tele- 
scope by  Lippersheitn :  its  application  to 
astronomy  by  Harriot,  Simon  Afarius,  and 

Galilei 149 

§  119.          The  Sidereus  Nuncius:  observations  of  the  moon     150 
§  120.          New  stars:  resolution  of  portions  of  the  Milky 

Way I5I 

§  121.  The  discovery  of  Jupiter's  satellites :  their  im- 
portance for  the  Coppernican  controversy : 
controversies  .  .  .  .  .151 

§  122.          Appointment  at  the  Tuscan  court       .        .        .     1 53 
§  123.          Observations    of    Saturn.      Discovery    of   the 

phases  of  Venus 154 

§  124.          Observations  of  sun-spots  by  Fabricius,  Harriot, 
Scheiner,  and  Galilei :  the  Macchie  Solari : 
proof  that  the  spots  were  not  planets :  obser- 
vations of  the  umbra  and  penumbra     .         .154 
§  125.     Quarrel  with  Scheiner  and  the  Jesuits  :  theological 
controversies :     Letter  to    the    Grand   Duchess 

Christine  157 

§126.     Visit  to  Rome.    The  first  condemnation  :  prohibition 

of  Coppernican  books 159 

§  127.     Method    for  finding    longitude.      Controversy  on 

comets:  // Saggiatore 1 60 

§  128.    Dialogue  on  the  Two  Chief  Systems  of  the  World. 

Its  preparation  and  publication    .         .         .162 
§  129.          The  speakers :  argument  for  the  Coppernican 
system  based  on  the  telescopic  discoveries  : 
discussion  of  stellar  parallax  :  the  differential 
method  of  parallax 163 

b 


xviii  Contents 

PAGE 

§  130.  Dynamical  arguments  in  favour  of  the  motion  of 

the  earth :  the  First  Law  of  Motion.  The  tides  1 65 

§  131.  The  trial  and  condemnation.  The  thinly  veiled 
Coppernicanism  of  the  Dialogue :  the  re- 
markable preface 168, 

§  132.  Summons  to  Rome :  trial  by  the  Inquisition  : 

condemnation,  abjuration,  and  punishment  : 
prohibition  of  the  Dialogue  ....  169 

§  133.  Last  years:  life  at  Arcetri:  libration  of  the  moon  : 
the  Two  New  Sciences  :  uniform  acceleration,  and 
the  first  law  of  motion.  Blindness  and  death  .  172 

§  134.     Estimate  of  Galilei's  work  :  his  scientific  method   .     176 


CHAPTER  VII. 
KEPLER  (FROM  1571  A.D.  TO  1630  A.D.),  §§  135-151      .    179-197 

§135.     Early  life  and  theological  studies      .         .         .         .179 

§  136.  Lectureship  on  mathematics  at  Gratz  :  astronomical 
studies  and  speculations :  the  Mysterium  Cosmo- 

graphicum 180 

•  §  137.     Religious  troubles  in  Styria:  work  with  Tycho       .     181 

§  138.  Appointment  by  the  Emperor  Rudolph  as  successor 
to  Tycho  :  writings  on  the  new  star  of  1604  and 
on  Optics  :  theory  of  refraction  and  a  new  form 
of  telescope 182 

§  139.     Study  of  the  motion  of  Mars  :  unsuccessful  attempts 

to  explain  it 183 

§§  140-1.  The  ellipse:  discovery  of  the  first  two  of  Kepler s 
Laws  for  the  case  of  Mars :  the  Commentaries 
on  Mars  * 184 

§  142.     Suggested  extension  of  Kepler's  Laws  to  the  other 

planets .         .     186 

S  143.     Abdication  and  death  of  Rudolph  :  appointment  at 

Linz 188 

§  144.     The  Harmony  of  the  World:  discovery  of  Kepler's 

Third  Law :  the  "  music  of  the  spheres  "     .         .188 

§  145.  Epitome  of  the  Copernican  Astronomy :  its  pro- 
hibition :  fanciful  correction  of  the  distance  of 
the  sun  :  observation  of  the  sun's  corona  .  .  191 

§  146.     Treatise  on  Comets  .         .         .         .         .         .  193 

§  147.     Religious  troubles  at  Linz  :   removal  to  Ulm   .         .     194 


Contents  xix 

PAGE 

§  148.  The  Rudolphine  Tables .194 

§  149.  Work  under  Wallenstein  :  death     ....     195 

§150.  Minor  discoveries :  speculations  on  gravity     .         .     195 

§151.  Estimate  of  Kepler's  work  and  intellectual  character     197 


CHAPTER  VIII. 
FROM  GALILEI  TO  NEWTON  (FROM  ABOUT   1638  A.D.  TO 

ABOUT    1687   A.D.),    §§    152-163 198-209 

§  152.  The  general  character  of  astronomical  progress 

during  the  period 198 

§  153.  Scheiner's  observations  oifaculae  on  the  sun.  Hevel: 
his  Selenographia  and  his  writings  on  comets  : 
his  star  catalogue.  Riccioli's  New  Almagest  .  198 

§  154.  Planetary  observations:  Huygens's  discovery  of  a 

satellite  of  Saturn  and  of  its  ring  .  .  .  199 

§  155.  Gascoigne's  and  AuzouCs  invention  of  the  micro- 
meter :  PicarcTs  telescopic  "  sights  "  .  .  .  202 

§  156.  Hotrocks  :  extension  of  Kepler's  theory  to  the 

moon  :  observation  of  a  transit  of  Venus  .  .  202 

§§  *57~8.  Huygens's  rediscovery  of  the  pendulum  clock  : 

his  theory  of  circular  motion  ....  203 

§  159.  Measurements  of  the  earth  by  Snell,  Norwood,  and 

Picard  .  .  .  .  .  .  204 

§  1 60.  The  Paris  Observatory  :  Domenico  Cassini:  his 
discoveries  of  four  new  satellites  of  Saturn  :  his 
other  work  ........  204 

§  161.  Richer s  expedition  to  Cayenne:  pendulum  observa- 
tions :  observations  of  Mars  in  opposition  :  hori- 
zontal parallax '.  annual  or  stellar  parallax  .  .  205 

§  162.     Roemcr  and  the  velocity  of  light       ....     208 

§  163.     Descartes  .......         .         ,208 


CHAPTER    IX. 

UNIVERSAL  GRAVITATION  (FROM  1643  A.D.  TO  1727  A.D.), 

§§  164-195          210-246 

§164.     Division  of  Newton's  life  into  three  periods      .         .     210 

§  165.     Early  life,  1643  to  1665 2IO 

§  166.     Great  productive  period,  1665-87     .         .         .         .211 


xx  Confers 

PAGE 

§  167.    Chief  divisions  of  his  work  :  agronomy,  optics,  pure 

mathematics         .         .         .         .         .         .         .211 

§  168.     Optical    discoveries :     the    reflecting    telescopes    of 

Gregory  and  Newton  :  the  spectrum     .         .         .211 
§169.     Newton's  description  of  his  discoveries  in  1665-6    .     212 
§  170.'   The   beginning   of  his   work   on  gravitation  :  the 
falling    apple :    previous    contributions    to    the 
subject  by  Kepler,  Borelli,  and  Huygens       .         .213 
§171.     The  problem  of  circular  motion  :  acceleration   .         .214 
§  172.     The  law  of  the  inverse  square  obtained  from  Kepler's 
Third  Law  for  the  planetary  orbits,  treated  as 

circles. 215 

§  173.     Extension  of  the  earth's  gravity  as  far  as  the  moon : 

imperfection  of  the  theory  .         .         .         .         .217 
§  174.     Hooke's  and  Wrens  speculations  on  the  planetary 
motions  and  on  gravity.    Newton's  second  calcu- 
lation of  the  motion  of  the  moon  :   agreement 

with  observation 221 

§  175-6.     Solution    of   the    problem   of   elliptic    motion  : 

Halleys  visit  to  Newton 221 

§  177.     Presentation  to  the  Royal  Society  of  the  tract  De 

Motu  :  publication  of  the  Principia      .         .         .     222 

§178.     The  Principia :  its  divisions 223 

§§  179-80.   The  Laws  of  Motion',  the  First  Law:  accelera- 
tion in  its  general  form  :   mass  and  force  : 

the  Third  Law 223 

§  181.  Law  of  universal  gravitation  enunciated     .         .     227 

§182.  The  attraction  of  a  sphere 228 

§  183.  The   general    problem   of    accounting    for   the 

motions  of  the  solar  system  by  means  of 
gravitation    and     the     Laws     of    Motion: 

perturbations 229 

§  184.  Newton's  lunar  theory         .         .         ...     230 

§  185.  Measurement  of  the  mass  of  a  planet  by  means 

of  its  attraction  of  its  satellites    .         .         .231 
§  186.  Motion  of  the  sun  :  centre  of  gravity  of  the  solar 

system:  relativity  of  motion         .         .         .231 
§  187.  The  non-spherical  form  of  the  earth,  and  of  Jupiter     233 

§  188.  Explanation  of  precession 234 

§  189.  The  tides  :  the  mass  of  the  moon  deduced  from 

tidal  observations 235 

§  190.          The  motions  of  comets  :  parabolic  orbits     .        .     237 


Contents  xxi 

PAGE 

§191.     Reception  of  the  Principia 239 

§  192.  Third  period  of  Newton's  life,  1687-1727:  Parlia- 
mentary career :  improvement  of  the  lunar 
theory :  appointments  at  the  Mint  and  removal 
to  London  :  publication  of  the  Optics  and  of  the 
second  and  third  editions  of  the  Principia,  edited 
by  Cotes  and  Pemberton  :  death  .  .  .  240 

§  193.  Estimates  of  Newton's  work  by  Leibniz,  by  Lagrange, 

and  by  himself 241 

§  194.  Comparison  of  his  astronomical  work  with  that  of 
his  predecessors  :  "  explanation  "  and  "  de- 
scription "  :  conception  of  the  material  universe 
as  made  up  of  bodies  attracting  one  another 
according  to  certain  laws 242 

§  195.     Newton's  scientific  method  :  "  Hypotheses  nonfingo  "     245 


CHAPTER  X. 

OBSERVATIONAL      ASTRONOMY     IN      THE     EIGHTEENTH 

CENTURY,  §§  196-227 247-286 

§  196.     Gravitational    astronomy:     its    development    due 
almost  entirely  to  Continental  astronomers  :  use 
of  analysis :  English  observational  astronomy     .  247 
§§  !97~8.     Flamsteed :    foundation  of  the   Greenwich  Ob- 
servatory: his  star  catalogue      ....  249 
§  199.     Halley  :  catalogue  of  Southern  stars        .        .         .  253 

§  200.           Halley's  comet 253 

§  2O I.           Secular  acceleration  of  the  moon's  mean  motion    .  254 

§  2O2.           Transits  of  Venus 254 

§  203.           Proper  motions  of  the  fixed  stars          .         .         .  255 
§§  204-5.     Lunar  and   planetary  tables  :  career  at  Green- 
wich :  minor  work 255 

§  206.     Bradley  :  career 257 

§§207-11.  Discovery  and   explanation   of  aberration',   the 

constant  of  aberration 258 

§  212.           Failure  to  detect  parallax    ...                  .  265 

§§213-5.     Discovery  of  nutation  :  Machin  ....  265 

§§  216-7.     Tables  of  Jupiter's  satellites  by  Bradley  and  by 
Wargentin  :    determination    of    longitudes, 

and  other  work    ......  269 

§  2i8.  His  observations  :  reduction         .        .         .         .271 


xxii  Contents 

%  PAGE 

§  219.     The  density  of  the  earth  :  Maskelyne  :  the  Cavendish 

experiment .273 

§  22O.  The  Cassini-Maraldi  school  in  France  .  .  .275 
§  221.  Measurements  of  the  earth :  the  Lapland  and 

Peruvian  arcs  :  Maupertnis  ...  .  .  -275 
§§  222-4.  Lacaille  :  his  career  :  expedition  to  the  Cape  : 

star  catalogues,  and  other  work  ....  2/9 
§§  225-6.  Tobias  Mayer  :  his  observations  :  lunar  tables  : 

the  longitude  prize  .  .  .  •."  "  .  .  282 

§227.  The  transits  of  Venus  in  1761  and  1769:  distance 

of  the  sun    v,      .         .        .         .        .         .        .     284 


CHAPTER  XI. 

GRAVITATIONAL  ASTRONOMY  IN  THE  EIGHTEENTH  CENTURY, 

§§228-250          .       .        ;.•-.       .        .     ;.        .   287-322 

§  228.  Newton's  problem  :  the  problem  of  three  bodies  : 
methods  of  approximation  :  lunar  theory  and 
planetary  theory  .  ,  .  ,  .  .  .  .  287 
229.  The  progress  of  Newtonian  principles  in  France  : 
popularisation  by  Voltaire.  The  five  great 
mathematical  astronomers  :  the  pre-eminence  of 
France  V  -  .  .  .  ..  '.  .  .  290 

§  230.     Euler :    his   career :    St.    Petersburg   and    Berlin  : 

extent  of  his  writings  .         .         .         .         .         .291 

§  231,     Clairaut'.   figure  of  the  earth  :  return  of  Halley's 

comet.         ,     '  ..      "„.- .  •    .         .         .         .  .  ••'    .     293 

§232.  D1  Alembert \  his  dynamics:  precession  and  nuta- 
tion :  his  versatility ;  rivalry  with  Clairaut  .  295 

§§  233~4-  The  lunar  theories  and  lunar  tables  of  Euler, 
Clairaut,  and  D'Alembert :  advance  on  Newton's 
lunar  theory  .......  297 

§  235.     Planetary  theory  :    Clairaut's  determination  of  the 

masses  of  the  moon  and  of  Venus  :  Lalande       .     299 

§  236.     Euler's  planetary  theory  :  method  of  the  variation 

of  elements  or  parameters     .         .         .         .         .     301 

§  237.     Lagrange :    his    career :    Berlin    and    Paris :    the 

Mecanique  Analytique  .         .         .         .         .     3^4 

§  238.  Laplace :  his  career  :  the  Mecanique  Celeste  and  the 
Systeme  du  Monde  \  politic.il  appointments  and 
distinctions  .  .  .  ./  \  .  a  .  3°6 


Contents  xxiii 

PAGE 

§  239.  Advance  made  by  Lagrange  and  Laplace  on  the 

work  of  their  immediate  predecessors  .  .  308 

§  240.  Explanation  of  the  moon's  secular  acceleration  by 

Laplace 308 

§  241.  Laplace's  lunar  theory:  tables  of  Burg  and  Burck- 

hardt 309 

§242.     Periodic  and  secular  inequalities       .         .         .         .310 

§  243.  Explanation  of  the  mutual  perturbation  of  Jupiter 

and  Saturn  :  long  inequalities  .  .  .  .312 

§§  244-5.  Theorems  on  the  stability  of  the  solar  system: 

the  eccentricity  fund  and  the  inclination  fund  .  313 

§246.     Tne  magnitudes  of  some  of  the  secular  inequalities     3*8 

§247.  Periodicil  inequalities:  solar  and  planetary  tables 

based  on  the  Me'canique  Celeste  .  .  .  .318 

§  248.  Minor  problems  of  gravitational  astronomy  :  the 
satellites  :  Saturn's  ring :  precession  and  nuta- 
tion :  figure  of  the  earth  :  tides  :  comets  :  masses 
of  planets  and  satellites  .....  318 

§  249.  The  solution  of  Newton's  problem  by  the  astro- 
nomers of  the  eighteenth  century  .  .  .  319 

§  250.     The  nebular  hypothesis :  its  speculative  character     .     320 


CHAPTER   XII. 
HERSCHEL  (FROM  1738  A.D.  TO  1822  A.D.),  §§  251-271  .  323-353 

§§  251-2.  William  Herschel's  early  ^career  :  Bath  :  his 

first  telescope 323 

§§  253~4-  The  discovery  of  the  planet  Uranus,  and  its 

consequences  :  Herschel's  removal  to  Slough  .  325 

§  255.  Telescope-making  :  marriage  :  the  forty-foot  tele- 
scope :  discoveries  of  satellites  of  Saturn  and  of 
Uranus 327 

§  256.  Life  and  work  at  Slough  :  last  years  :  Caroline 

Herschel 328 

§  257.  Herschel's  astronomical  programme  :  the  study  of 

the  fixed  stars  .  330 

§  258.  The  distribution  of  the  stars  in  space  :  star- 
gauging  :  the  "  grindstone "  theory  of  the 
universe :  defects  of  the  fundamental  assump- 
tion :  its  partial  withdrawal.  Employment  of 


xxiv  Contents 

PAGE 

brightness  as  a  test  of  nearness  :  measurement 
of  brightness  :  "  space-penetrating  "  power  of  a 
telescope 332 

§  259.  Nebulae  and  star  clusters  :  Herschel's  great  cata- 
logues  336 

§260.  Relation  of  nebulae  to  star  clusters:  the  "island 
universe  "  theory  of  nebulae  :  the  "  shining  fluid  " 
theory:  distribution  of  nebulae.  .  .  .  337 

§261.     Condensation  of  nebulae  into  clusters  and  stars       .     339 

§262.     The  irresolvability  of  the  Milky  Way       .         .         .     340 

§  263.  Double  stars  :  their  proposed  employment  for  find- 
ing parallax  :  catalogues  :  probable  connection 
between  members  of  a  pair  .  .  .  .341 

§  264.     Discoveries   of    the    revolution   of    double   stars : 

binary  stars  :  their  uselessness  for  parallax          .     343 

§  265.     The   motion   of    the    sun   in   space  :    the   various 

positions  suggested  for  the  apex  ....     344 

§266.  Variable  stars:  Mira  and  Algol:  catalogues  of 
comparative  brightness:  method  of  sequences'. 
variability  of  a  Herculis 346 

§  267.     Herschel's  work  on  the  solar  system  :  new  satellites : 

observations  of  Saturn,  Jupiter,  Venus,  and  Mars     348 

§  268.    Observations  of  the  sun  :  Wilson  :   theory  of  the 

structure  of  the  sun     .       • 350 

§269.     Suggested  variability  of  the  sun       .        .        .        .     351 

§  270.     Other  researches 352 

§  271.     Comparison  of  Herschel  with  his  contemporaries  : 

Schroeter, 352 

CHAPTER    XIII. 

THE  NINETEENTH  CENTURY,  §§  272-320       .       .       .    354-409 

§  272.  The  three  chief  divisions  of  astronomy,  observa- 
tional, gravitational,  and  descriptive  .  -  .  .  354 

§  273.  The  great  growth  of  descriptive  astronomy  in  the 

nineteenth  century 355 

§274.     Observational  Astronomy.    Instrumental  advances: 

the  introduction  of  photography  .         .         .     357 
§275.  The  method  of  least  squares  :  Legendre  and  Gauss     357 

§  276.  Other  work  by  Gauss  :   the  Theoria  Motus  :  re- 

discovery of  the  minor  planet  Ceres     .         .     358 


Contents  xxv 

PAGE 

§  277.  Bessel :    his    improvement    in    methods   of   re- 

duction :  his  table  of  refraction  :  the  Funda- 
menta  Nova  and  Tabulae  Regiomontanae      .     359 
§278.  The  para' lax  of  6 1  Cygni '.  its  distance        .         .     360 

§  279.          Henderson's  parallax  of  a  Centauri  and  Struve's 

of  Vega  :  later  parallax  determinations        .     362 
§  280.  Star  catalogues  :  the  photographic  chart    .         .     362 

§§  281-4.  The  distance  of  the  sun  :  transits  of  Venus  : 
observations  of  Mars  and  of  the  minor  planets 
in  opposition  :  diurnal  method :  gravitational 
methods,  lunar  and  planetary :  methods 
based  on  the  velocity  of  light :  summary  of 

results 363 

§  285.  Variation  in  latitude  :  rigidity  of  the  earth          .     367 

§  286.  Gravitational  Astronomy.  Lunar  theory  :  Damoi- 
seau,Poisson,  Ponte'coulant,  Lubbock,Hansen, 
Delaunay,  Professor  Newcomb,  Adams,  Dr. 
Hill 367 

§  287.  Secular  acceleration  of  the  moon's  mean  motion  : 

Adams's  correction  of  Laplace  :  Delaunay's 
explanation  by  means  of  tidal  friction  .  .  369 

§  288.  Planetary  theory  :  Leverrier,  Gylden,  M.  Poincare     370 

§  289.  The  discovery  of  Neptune  by  Leverrier  and  Dr. 

Galle  :  Adams's  work 37 l 

§  290.  Lunar  and  planetary  tables  :  outstanding  dis- 

crepancies between  theory  and  observation  372 

§  291.  Cometary  orbits  :  return  of  Halley's  comet  in 

1835  :  Encke's  and  other  periodic  comets  .  372 

§  292.  Theory  of  tides  :  analysis  of  tidal  observations 
by  Lubbock,  Whewell,  Lord  Kelvin,  and 
Professor  Darwin  :  bodily  tides  in  the  earth 
and  its  rigidity 373 

§293.  The  stability  of  the  solar  system          .         .         .     374 

§  294.  Descriptive  Astronomy.  Discovery  of  the  minor 
planets  or  asteroids :  their  number,  dis- 
tribution, and  size 37° 

§  295.  Discoveries  of  satellites  of  Neptune,  Saturn, 
Uranus,  Mars,  and  Jupiter,  and  of  the  crape 
ring  of  Saturn 380 

§  296.  The  surface  of  the  moon  :  nils :  the  lunar  atmo- 
sphere   382 


xxvi  Contents 

PAGE 

§  297.  The  surfaces  of  Mars,  Jupiter,  and  Saturn  :    the 

canals  on  Mars  :  Maxwell's  theory  of  Saturn's 
rings  :  the  rotation  of  Mercury  and  of  Venus  383 

§  298.  The  surface  of  the  sun  :  Schwabe's  discovery  of 

the  periodicity  of  sun-spots  :  connection  be- 
tween sun-spots  and  terrestrial  magnetism: 
Carringtorfs  observations  of  the  motion  and 
distribution  of  spots :  Wilson's  theory  of  spots  385 

§§  299-3°°.  Spectrum  analysis:   Newton,  Wollaston^  Frann- 

hofer,  Kirchhoff  :  the  chemistry  of  the  sun  .     386 

§  301.  Eclipses  of  the  sun  :  the  corona,  chromosphere, 
and  prominences :  spectroscopic  methods  of 
observation  .  389 

§  302.  Spectroscopic  method  of  determining  motion  to 
or  from  the  observer :  Doppler's  principle  : 
application  to  the  sun 391 

§  3°3-          The  constitution  of  the  sun          .  .         .     392 

§§  3°4~5-  Observations  of  comets  :  nucleus  :  theory  of  the 
formation  of  their  tails  :  their  spectra  :  re- 
lation between  comets  and  meteors  .  .  393 

§§  3°6-8.  Sidereal  astronomy  :  career  of  John  Herschel :  his 
catalogues  of  nebulae  and  of  double  stars  : 
the  expedition  to  the  Cape  :  measurement  of 
the  sun's  heat  by  Herschel  and  by  Pouillet .  396 

§  3^9-  Double     stars :    observations    by    Struve    and 

others :  orbits  of  binary  stars       .         .         .     398 

§310.  Lord  Rosse's  telescopes:  his  observations  of 
nebulae  :  revival  of  the  "island  universe  " 
theory 400 

§  311'  Application   of  the   spectroscope   to    nebulae: 

distinction  between  nebulae  and  clusters     .     401 

§312.  Spectroscopic  classification  of  stars  by  Secchi : 
chemistry  of  stars  :  stars  with  bright-line 
spectra 401 

§§  3I3-4'  Motion  of  stars  in  the  line  of  sight.  Discovery 
of  binary  stars  by  the  spectroscope  :  eclipse 
theory  of  variable  stars  ....  402 

§315.  Observations  of  variable  stars     ....     403 

§316.  Stellar  photometry:  Pogsorfs  light  ratio:    the 

Oxford,  Harvard,  and  Potsdam  photometries    403 

§317.  Structure  of  the  sidereal  system:  relations   of 

stars  and  nebulae 405 


Contents  xxvii 

PAGE 

§§  318-20.  Laplace's  nebular  hypothesis  in  the  light  of 
later  discoveries :  the  sun's  heat :  Helmholiz's 
shrinkage  theory.  Influence  of  tidal  friction  on 
the  development  of  the  solar  system  :  Professor 
Darwin's  theory  of  the  birth  of  the  moon. 
Summary 406 

LIST  OF  AUTHORITIES  AND  OF  BOOKS  FOR  STUDENTS.        .    411 

INDEX  OF  NAMES 4*7 

GENERAL  INDEX 425 


LIST    OF    ILLUSTRATIONS. 


FIG.  PAGE 

The  moon  Frontispiece 

1.  The  celestial  sphere         ...         ...  5 

2.  The  daily  paths  of  circumpolar  stars To  face  p.  8 

3.  The  circles  of  the  celestial  sphere       9 

4.  The  equator  and  the  ecliptic     II 

5.  The  Great  Bear To  face  p.  12 

6.  The  apparent  path  of  Jupiter 16 

7.  The  apparent  path  of  Mercury  ...         ...  17 

8- 1 1.  The  phases  of  the  moon      30,  31 

12.  The  curvature  of  the  earth        32 

13.  The  method  of  Aristarchus  for  comparing  the  distances  of 

the  sun  and  moon       ...         ...         ...  34 

14.  The  equator  and  the  ecliptic 36 

15.  The  equator,  the  horizon,  and  the  meridian 38 

16.  The  measurement  of  the  earth  ...         39 

17.  The  eccentric       • 44 

1 8.  The  position  of  the  sun's  apogee         ...  45 

19.  The  epicycle  and  the  deferent ...  47 

20.  The  eclipse  method  of  connecting  the  distances  of  the  sun 

and  moon         5° 

21.  The  increase  of  the  longitude  of  a  star          ...  52 

22.  The  movement  of  the  equator ...         53 

23.  24.  The  precession  of  the  equinoxes    ...         53>  54 

25.  The  earth's  shadow         57 

26.  The  ecliptic  and  the  moon's  path         ...  57 

27.  The  sun  and  moon           v         ...  58 

28.  Partial  eclipse  of  the  moon        5^ 

29.  Total  eclipse  of  the  moon          ...         58 

30.  Annular  eclipse  of  the  sun         ...         59 

31.  Parallax     ...         ...         ...         .».         ...         60 

32.  Refraction  by  the  atmosphere 63 


xxx  List  of  Illustrations 

FIG.  PA1E 

33.  Parallax 08 

34.  Jupiter's  epicycle  and  deferent ...         ...         ...  70 

35.  Theequant           71 

36.  The  celestial  spheres       ...         ...         ...  89 

PORTRAIT  OF  COPPERNICUS        ...         ...         ...        To  face  p.  94 

37.  Relative  motion ...         ...         ...         ...         ...  102 

38.  The  relative  motion  of  the  sun  and  moon      ...         ...         ...  103 

39.  The  daily  rotation  of  the  earth             ...         ...  104 

40.  The  solar  system  according  to  Coppernicus ...  107 

41.  42.  Coppernican  explanation  of  the  seasons  ...         ...        108,   109 

43.  The  orbits  of  Venus  and  of  the  earth ...         ...  113 

44.  The  synodic  and  sidereal  periods  of  Venus   ...         ...         ...  114 

45.  The  epicycle  of  Jupiter  ...         ...         ...         ...  116 

46.  The  relative  sizes  of  the  orbits  of  the  earth  and  of  a  superior 

planet   ...         ...         ...         ...         ...         ...         ...         ...  117 

47.  The  stationary  points  of  Mercury         ...         119 

48.  The  stationary  points  of  Jupiter           ...         ...         ...         ...  120 

49.  The  alteration  in   a  planet's  apparent  position  due  to  an 

alteration  in  the  earth's  distance  from  the  sun    ...         ...  122 

50.  Stellar  parallax 124 

51.  Uraniborg             ...         133 

52.  Tycho's  system  of  the  world     ...         ...  137 

PORTRAIT  OF  TYCHO  BRAHE     ...         ...         ...         To  face  p.  139 

53.  One  of  Galilei's  drawings  of  the  moon           ...                M  150 

54.  Jupiter  and  its  satellites  as  seen  on  January  7,  1610            ...  152 

55.  Sun-spots...          ...         ...          ...          ...          ...         To  face  p.  154 

56.  Galilei's  proof  that  sun-spots  are  not  planets            ...         ...  F56 

57.  The  differential  method  of  parallax      165 

PORTRAIT  OF  GALJLEI     ...         ...        To  face  p.  171 

58.  The  daily  libration  of  the  moon            ...          ....          ...          ...  173 

PORTRAIT  OF  KEPLER    ...         ...         To  face  p.  183 

59.  An  ellipse...         ...         ...         ...         ...         ...  185 

60.  Kepler's  second  law        ...         ...  186 

61.  Diagram  used  by  Kepler  to  establish  his  laws  of  planetary 

motion ...         ...         ...  187 

62.  The  "  music  of  the  spheres     according  to  Kepler     ...         ...  190 

63.  Kepler's  idea  of  gravity ...          ...          ...  196 

64.  Saturn's  ring,  as  drawn  by  Huygens   ...          ...        To  face  p.  2OO 

65.  Saturn,  with  the  ring  seen  edge-wise              ...                „  2OO 

66.  The  phases  of  Saturn's  ring       ...          ...          ...          ...          ...  201 

67.  Early  drawings  of  Saturn           ...         ...         ...        To  face  p.  202 

68.  Mars  in  opposition           ...         ...         ...  206 


List  of  Illustrations  xx:;i 

FIG.  PAGE 

09.  The  parallax  of  a  planet           ...         ...         ...  206 

70.  Motion  in  a  circle          ...         ...         ...         ...  214 

71.  The  moon  as  a  projectile          ...         ...         ...         ...         ...  220 

72.  The  spheroidal  form  of  the  earth        234 

73.  An  elongated  ellipse  and  a  parabola  ...         ...         ...         ...  238 

PORTRAIT  OF  NEWTON  ...         ...         ...         ...        To  face  p.  240 

PORTRAIT  OF  BRADLEY            ,,  258 

74.  75.  The  aberration  of  light       262,263 

76.  The  aberrational  ellipse            ...         ...         ...  264 

77.  Precession  and  nutation           268 

78.  The  varying  curvature  of  the  earth 277 

79.  Tobias  Mayer's  map  of  the  moon        ...         ...         To  face  p,  282 

80.  The  path  of  Halley's  comet     294 

81.  A  varying  ellipse           ...         ...         ...         ...  303 

PORTRAIT  OF  LAGRANGE          ...         ...         ...        To  face  p.  305 

PORTRAIT  OF  LAPLACE...         ...         ...         ...               „  307 

PORTRAIT  OF  WILLIAM  HERSCHEL     ,,  327 

82.  Herschel's  forty-foot  telescope           ...         ...         ...         ...  329 

83.  Section  of  the  sidereal  system            ...         ...  333 

84.  Illustrating  the  effect  of  the  sun's  motion  in  space...         ...  345 

85.  61  Cygni  and  the  two  neighbouring  stars  used  by  Bessel  ...  360 

86.  The  parallax  of  6 1  Cygni         ...         ...         ...  361 

87.  The  path  of  Halley's  comet      ...  373 

88.  Photographic  trail  of  a  minor  planet  ...         ...         To  face  p.  377 

89.  Paths  of  minor  planets...         ...         ...         ...         ...         ...  378 

90.  Comparative  sizes  of  three  minor  planets  and  the  moon    ...  379 

91.  Saturn  and  its  system  ...         ...         ...         ...  380 

92.  Mars  and  its  satellites 381 

93.  Jupiter  and  its  satellites           ...         ...         ...  3^2 

94.  The  Apennines  and   the   adjoining  regions)      TQ  -  „ 

of  the  moon /        °  Jace  P-  33 

95.  Saturn  and  its  rings      ...         ...         ...         ...               ,,  384 

96.  A  group  of  sun-spots    ...         ...         „  385 

97.  Fraunhofer's  map  of  the  solar  spectrum        ...               „  387 

98.  The  total  solar  eclipse  of  1886            ...          ...               ,,  390 

99.  The  great  comet  of  1882           ...         ...         ...               „  393 

100.  The  nebula  about  ij  Argus      ...         ...         ...               „  397 

101.  The  orbit  of  £  Ursae     ...         ...         ...         ...         ...         ...  399 

102.  Spiral  nebulae    ...         ...         ...         ...         ...         To  face  p,  400 

103.  The  spectrum  of  /3  A urigae     ...         ...         ...               |f  403 

104.  The  Milky  Way  near  the  cluster  in  Perseus                  „  405 


A  SHORT  HISTORY  OF  ASTRONOMY. 


CHAPTER   I. 

PRIMITIVE   ASTRONOMY. 

"The  never-wearied  Sun,  the  Moon  exactly  round, 
And  all   those  Stars  with  which   the   brows   of  ample   heaven  are 

crowned, 

Orion,  all  the  Pleiades,  and  those  seven  Atlas  got, 
The  close  beamed  Hyades,  the  Bear,  surnam'd  the  Chariot, 
That  turns  about  heaven's  axle  tree,  holds  ope  a  constant  eye 
Upon  Orion,  and  of  all  the  cressets  in  the  sky 
His  golden  forehead  never  bows  to  th'  Ocean  empery." 

The  Iliad  (Chapman's  translation). 

i.  ASTRONOMY  is  the  science  which  treats  of  the  sun,  the 
moon,  the  stars,  and  other  objects  such  as  comets  which  are 
seen  in  the  sky.  It  deals  to  some  extent  also  with  the  earth, 
but  only  in  so  far  as  it  has  properties  in  common  with  the 
heavenly  bodies.  In  early  times  astronomy  was  concerned 
almost  entirely  with  the  observed  motions  of  the  heavenly 
bodies.  At  a  later  stage  astronomers  were  able  to  discover 
the  distances  and  sizes  of  many  of  the  heavenly  bodies, 
and  to  weigh  some  of  them ;  and  more  recently  they  have 
acquired  a  considerable  amount  of  knowledge  as  to  their 
nature  and  the  material  of  which  they  are  made. 

2.  We  know  nothing  of  the  beginnings  of  astronomy, 
and  can  only  conjecture  how  certain  of  the  simpler  facts 
of  the  science — particularly  those  with  a  direct  influence  on 
human  life  and  comfort — gradually  became  familiar  to  early 
mankind,  very  much  as  they  are  familiar  to  modern  savages. 


*    «A\  i:  ^v  J  J'  J-4 ; Short  History  of  Astronomy  [Cn.  I. 

With  these  facts  it  is  convenient  to  begin,  taking  them  in 
the  order  in  which  they  most  readily  present  themselves  to 
any  ordinary  observer. 

3.  The  sun  is  daily  seen  to  rise  in  the  eastern  part  of 
the  sky,  to  travel  across  the  sky,  to  reach  its  highest  position 
in  the  south  in  the  middle  of  the  day,  then  to  sink,  and 
finally  to  set  in  the  western  part  of  the  sky.     But  its  daily 
path  across  the  sky  is  not  always  the  same :  the  points  of 
the  horizon  at.  which  it  rises  and  sets,  its  height  in  the  sky 
at  midday,  and  the  time  from  sunrise  to   sunset,  all  go 
through  a  series   of  changes,  which  are  accompanied  by 
changes  in  the  weather,  in  vegetation,  etc.;  and  we   are 
thus  able  to  recognise  the  existence  of  the  seasons,  and 
their  recurrence  after  a  certain  interval  of  time  which  is 
known  as  a  year. 

4.  But  while  the  sun  always  appears  as  a  bright  circular 
disc,  the  next  most  conspicuous  of  the  heavenly  bodies,  the 
moon,  undergoes  changes  of  form  which  readily  strike  the 
observer,  and  are  at  once  seen  to  take  place  in  a  regular  order 
and  at  about  the  same  intervals  of  time.    A  little  more  care, 
however,  is  necessary  in  order  to  observe  the  connection 
between  the  form  of  the  moon  and  her  position  in  the  sky 
with  respect  to  the   sun.     Thus  when  the  moon  is  first 
visible  soon  after  sunset  near  the  place  where  the  sun  has  set, 
her  form  is  a  thin  crescent  (cf.  fig.  n  on  p.  31),  the  hollow 
side  being  turned  away  from  the  sun,  and  she  sets  soon 
after  the  sun.     Next  night  the  moon  is   farther  from  the 
sun,  the  crescent  is  thicker,  and  she  sets  later ;  and  so  on, 
until  after  rather  less  than  a  week  from  the  first  appearance 
of  the  crescent,  she  appears  as   a  semicircular  disc,   with 
the  flat  side  turned  away  from  the  sun.     The  semicircle 
enlarges,  and  after  another  week  has  grown  into  a  complete 
disc ;  the  moon  is  now  nearly  in  the  opposite  direction  to 
the  sun,  and  therefore  rises  about  at  sunset  and  sets  about 
at  sunrise.     She  then  begins  to  approach  the  sun  on  the 
other  side,  rising  before  it  and   setting  in   the   daytime  \ 
her  size  again  diminishes,  until  after  another  week  she  is 
again  semicircular,  the  flat  side   being  still   turned   away 
from   the   sun,  but   being   now   turned   towards   the   west 
instead  of  towards  the  east.    The  semicircle  then  becomes 
a  gradually  diminishing  crescent,  and   the   time   of  rising 


$$3-6]  The  Beginnings  of  Astronomy  3 

approaches  the  time  of  sunrise,  until  the  moon  becomes 
altogether  invisible.  After  two  or  three  nights  the  new 
moon  reappears,  and  the  whole  series  of  changes  is  repeated. 
The  different  forms  thus  assumed  by  the  moon  are  now 
known  as  her  phases ;  the  time  occupied  by  this  series  of 
changes,  the  month,  would  naturally  suggest  itself  as  a  con- 
venient measure  of  time ;  and  the  day,  month,  and  year 
would  thus  form  the  basis  of  a  rough  system  of  time- 
measurement. 

5.  From  a  few  observations  of  the  stars  it  could   also 
clearly  be  seen   that  they  too,  like   the   sun   and   moon, 
changed  their  positions  in  the  sky,  those  towards  the  east 
being  seen  to  rise,  and  those  towards  the  west  to  sink  and 
finally  set,  while  others  moved  across  the  sky  from  east  to 
west,  and  those  in  a  certain  northern  part  of  the  sky,  though 
also  in  motion,  were  never  seen  either  to  rise  or  set.  Although 
anything  like  a  complete  classification  of  the  stars  belongs 
to  a  more  advanced  stage  of  the  subject,  a  few  star  groups 
could  easily  be  recognised,  and  their  position  in  the  sky 
could  be  used  as  a  rough  means  of  measuring  time  at  night, 
just  as  the  position  of  the  sun  to  indicate  the  time  of  day. 

6.  To   these   rudimentary   notions   important   additions 
were  made  when  rather  more  careful  and  prolonged  obser- 
vations  became   possible,   and    some    little    thought    was 
devoted  to  their  interpretation. 

Several  peoples  who  reached  a  high  stage  of  civilisation 
at  an  early  period  claim  to  have  made  important  progress 
in  astronomy.  Greek  traditions  assign  considerable  astro- 
nomical knowledge  to  Egyptian  priests  who  lived  some 
thousands  of  years  B.C.,  and  some  of  the  peculiarities  of 
the  pyramids  which  were  built  at  some  such  period  are  at 
any  rate  plausibly  interpreted  as  evidence  of  pretty  accurate 
astronomical  observations ;  Chinese  records  describe  observa- 
tions supposed  to  have  been  made  in  the  25th  century  B.C.; 
some  of  the  Indian  sacred  books  refer  to  astronomical 
knowledge  acquired  several  centuries  before  this  time ;  and 
the  first  observations  of  the  Chaldaean.  priests  'of  Babylon 
have  been  attributed  to  times  not  much  later. 

On  the  other  hand,  the  earliest  recorded  astronomical 
observation  the  authenticity  of  which  may  be  accepted 
without  scruple  belongs  only  to  the  8th  century  B.C. 


4  A  Short  History  of  Astronomy  [CH.  t 

For  the  purposes  of  this  book  it  is  not  worth  while  to 
make  any  attempt  to  disentangle  from  the  mass  of  doubtful 
tradition  and  conjectural  interpretation  of  inscriptions,  bear- 
ing on  this  early  astronomy,  the  few  facts  which  lie  embedded 
therein ;  and  we  may  proceed  at  once  to  give  some  account 
of  the  astronomical  knowledge,  other  than  that  already  dealt 
with,  which  is  discovered  in  the  possession  of  the  earliest 
really  historical  astronomers — the  Greeks — at  the  beginning 
of  their  scientific  history,  leaving  it  an  open  question  what 
portions  of  it  were  derived  from  Egyptians,  Chaldaeans,  their 
own  ancestors,  or  other  sources. 

7.  If  an  observer  looks  at  the*  stars  on  any  clear  night 
he  sees  an  apparently  innumerable  *  host  of  them,  which 
seem  to  lie  on  a  portion  of  a  spherical  surface,  of  which  he 
is  the  centre.  This  spherical  surface  is  commonly  spoken 
of  as  the  sky,  and  is  known  to  astronomy  as  the  celestial 
sphere.  The  visible  part  of  this  sphere  is  oounded  by  the 
earth,  so  that  only  half  can  be  seen  at  once  ;  but  only  the 
slightest  effort  of  the  imagination  is  required  to  think  of 
the  other  half  as  lying  below  the  earth,  and  containing  other 
stars,  as  well  as  the  sun.  This  sphere  -appears  to  the 
observer  to  be  very  large,  though  he  is  incapable  of  forming 
any  precise  estimate  of  its  size,  f 

Most  of  us  at  the  present  day  have  been  taught  in  child- 
hood that  the  stars  are  at  different  distances,  and  that  this 
sphere  has  in  consequence  no-  real  existence.  The  early 
peoples  had  no  knowledge  of  this,  and  for  them  the  celestial 
/  sphere  really  existed,  and  was  often  thought  to  be  a  solid 
I  sphere  of  crystal. 

Moreover  modem  astronomers,  as  well  as  ancient,  find 
it  convenient  for  very  many  purposes  to  make  use  of  this 
sphere,  though  it  has  no  material  existence,  as  a  means 
of  representing  the  directions  in  which  the  heavenly  bodies 
are  seen  and  their  motions.  For  all  that  direct  observation 

*  In  our  climate  2,000  is  about  the  greatest  number  ever  visible 
at  once,  even  to  a  keen-sighted  person. 

f  Owing  to  the  greater  brightness  of  the  stars  overhead  they 
usually  seem  a  little  nearer  than  those  near  the  horizon,  and  con- 
sequently the  visible  portion  of  the  celestial  sphere  appears  to  be 
rather  less  than  a  half  of  a  complete  sphere.  This  is,  however,  of  no 
importance,  and  will  for  the  future  be  ignored. 


*  7]  •    The  Celestial  Sphere  5 

can  tell  us  about  the  position  of  such  an  object  as  a  star 
is  its  direction ;  its  distance  can  only  be  ascertained  by 
indirect  methods,  if  at  all.  If  we  draw  a  sphere,  and 
suppose  the  observer's  eye  placed  at  its  centre  o  (fig.  i), 
and  then  draw  a  straight  line  from  o  to  a  star  s,  meeting 
the  surface  of  the  sphere  in  the  point  s ;  then  the  star 
appears  exactly  in  the  same  position  as  if  it  were  at  s, 
nor  would  its  apparent  position  be  changed  if  it  were 
placed  at  any  other  point,  such  as  s'  or  s",  on  this  same 


FIG.  I. — The  celestial  sphere. 


line.  When  we  speak,  therefore,  of  a  star  as  being  at 
a  point  s  on  the  celestial  sphere,  all  that  we  mean  is  that 
it  is  in  the  same  direction  as  the  point  s,  or,  in  other 
words,  that  it  is  situated  somewhere  on  the  straight  line 
through  o  and  s.  The  advantages  of  this  method  of  repre- 
senting the  position  of  a  star  become  evident  when  we  wish 
to  compare  the  positions  of  several  stars.  The  difference 
of  direction  of  two  stars  is  the  angle  between  the  lines 
drawn  from  the  eye  to  the  stars ;  ^.,  if  the  stars  are  R,  s,  it 
is  the  angle  R  o  s.  Similarly  the  difference  of  direction  of 


6  A  Short  History  of  Astronomy  [Cn.  I. 

another  pair  of  stars,  p,  Q,  is  the  angle  P  o  Q.  The  two  stars 
P  and  Q  appear  nearer  together  than  do  R  and  s,  or  farther 
apart,  according  as  the  angle  p  o  Q  is  less  or  greater  than 
the  angle  R  o  s.  But  if  we  represent  the  stars  by  the 
corresponding  points/,  q,  r,  s  on  the  celestial  sphere,  then 
(by  an  obvious  property  of  the  sphere)  the  angle  P  o  Q 
(which  is  the  same  as  p  o  q)  is  less  or  greater  than  the 
angle  R  o  s  (or  r  o  s)  according  as  the  arc  joining  /  q 
on  the  sphere  is  less  or  greater  than  the  arc  joining  r  s, 
and  in  the  same  proportion  ;  if,  for  example,  the  angle  R  o  s 
is  twice  as  great  as  the  angle  p  o  Q,  so  also  is  the  arc  /  q 
twice  as  great  as  the  arc  r  s.  We  may  therefore,  in  all 
questions  relating  only  to  the  directions  of  the  stars,  replace 
the  angle  between  the  directions  of  two  stars  by  the  arc 
joining  the  corresponding  points  on  the  celestial  sphere,  or, 
in  other  words,  by  the  distance  between  these  points  on 
the  celestial  sphere.  But  such  arcs  on  a  sphere  are 
easier  both  to  estimate  by  eye  and  to  treat  geometrically 
than  angles,  and  the  use  of  the  celestial  sphere  is  therefore 
of  great  value,  apart  from  its  historical  origin.  It  is  im- 
portant to  note  that  this  apparent  distance  of  two  stars, 
i.e.  their  distance  from  one  another  on  the  celestial  sphere, 
is  an  entirely  different  thing  from  their  actual  distance  from 
one  another  in  space.  In  the  figure,  for  example,  Q  is 
actually  much  nearer  to  s  than  it  is  to  p,  but  the  apparent 
distance  measured  by  the  arc  q  s  is  several  times  greater 
than  q  p.  The  apparent  distance  of  two  points  on  the 
celestial  sphere  is  measured  numerically  by  the  angle 
between  the  lines  joining  the  eye  to  the  two  points, 
expressed  in  degrees,  minutes,  and  seconds,* 

We  might  of  course  agree  to  regard  the  celestial  sphere 
as  of  a  particular  size,  and  then  express  the  distance  be- 
tween two  points  on  it  in  miles,  feet,  or  inches  ;  but  it  is 
practically  very  inconvenient  to  do  so.  To  say,  as  some 
people  occasionally  do,  that  the  distance  between  two  stars 
is  so  many  feet  is  meaningless,  unless  the  supposed  size  of 
the  celestial  sphere  is  given  at  the  same  time. 

It  has  already  been  pointed  out  that  the  observer  is 
always  at  the  centre  of  the  celestial  sphere ;  this  remains 

*  A  right  angle  is  divided  into  ninety  degrees  (90°),  a  degree  into 
sixty  minutes  (60'),  and  a  minute  into  sixty  seconds  (60"). 


*  8]  The  Celestial  Sphere :  its  Poles  7 

true  even  if  he  moves  to  another  place.  A  sphere  has, 
however,  only  one  centre,  and  therefore  if  the  sphere 
remains  fixed  the  observer  cannot  move  about  and  yet 
always  remain  at  the  centre.  The  old  astronomers  met 
this  difficulty  by  supposing  that  the  celestial  sphere  was  so 
large  that  any  possible  motion  of  the  observer  would  be 
insignificant  in  comparison  with  the  radius  of  the  sphere  and 
could  be  neglected.  It  is  often  more  convenient— when 
we  are  using  the  sphere  as  a  mere  geometrical  device  for 
representing  the  position  of  the  stars — to  regard  the  sphere 
as  moving  with  the  observer,  so  that  he  always  remains  at 
the  centre. 

8.  Although  the  stars  all  appear  to  move  across  the 
sky  (§  5),  and  their  rates  of  motion  differ,  yet  the  distance 
between  any  two  stars  remains  unchanged,  and  they  were  I 
consequently  regarded  as  being  attached  to  the  celestial  ! 
sphere.  Moreover  a  little  careful  observation  would  have 
shown  that  the  motions  of  the  stars  in  different  parts  of  the 
sky,  though  at  first  sight  very  different,  were  just  such 
as  would  have  been  produced  by  the  celestial  sphere — with 
the  stars  attached  to  it — turning  about  an  axis  passing 
through  the  centre  and  through  a  point  in  the  northern 
sky  close  to  the  familiar  pole-star.  This  point  is  called 
the  pole.  As,  however,  a  straight  line  drawn  through  the 
centre  of  a  sphere  meets  it  in  two  points,  the  axis  of 
the  celestial  sphere  meets  it  again  in  a  second  point, 
opposite  the  first,  lying  in  a  part  of  the  celestial  sphere 
which  is  permanently  below  the  horizon.  This  second 
point  is  also  called  a  pole;  and  if  the  two  poles  have  to 
be  distinguished,  the  one  mentioned  first  is  called  the 
north  pole,  and  the  other  the  south  pole.  The  direction 
of  the  rotation  of  the  celestial  sphere  about  its  axis  is 
such  that  stars  near  the  north  pole  are  seen  to  move  round 
it  in  circles  in  the  direction  opposite  to  that  in  which  the 
hands  of  a  clock  move ;  the  motion  is  uniform,  and  a 
complete  revolution  is  performed  in  four  minutes  less  than  , 
twenty-four  hours  ;  so  that  the  position  of  any  star  in  the  \ 
sky  at  twelve  o'clock  to-night  is  the  same  as  its  position  at  • 
four  minutes  to  twelve  to-morrow  night. 

The  moon,  like   the  stars,   shares   this   motion   of  the 
celestial   sphere,  and  so  also   does   the   sun,   though   this 


8  A  Short  History  of  Agronomy  [Cn.  I. 

is  more  difficult  to  recognise  owing  to  the  fact  that  the  sun 
and  stars  are  not  seen  together. 

As  other  motions  of  the  celestial  bodies  have  to  be  dealt 
with,  the  general  motion  just  described  may  be  conveniently 
referred  to  as  the  daily  motion  or  daily  rotation  of  the 
celestial  sphere. 

9.  A  further  study  of  the  daily  motion  would  lead  to  the 
recognition  of  certain  important  circles  of  the  celestial  sphere. 

Each  star  describes  in  its  daily  motion  a  circle,  the  size 
of  which  depends  on  its  distance  from  the  poles.  Fig.  2 
shews  the  paths  described  by  a  number  of  stars  near  the 
pole,  recorded  photographically,  during  part  of  a  night. 
The  pole-star  describes  so  small  a  circle  that  its  motion  can 
only  with  difficulty  be  detected  with  the  naked  eye,  stars  a 
little  farther  off  the  pole  describe  larger  circles,  and  so  on, 
until  we  come  to  stars  half-way  between  the  two  poles,  which 
describe  the  largest  circle  which  can  be  drawn  on  the 
celestial  sphere.  The  circle  on  which  these  stars  lie  and 
which  is  described  by  any  one  of  them  daily  is  called  the 
equator.  By  looking  at  a  diagram  such  as  fig.  3,  or,  better 
still,  by  looking  at  an  actual  globe,  it  can  easily  be  seen 
that  half  the  equator  (E  Q  w)  lies  above  and  half  (the 
dotted  part,  w  R  E)  below  the  horizon,  and  that  in  conse- 
quence a  star,  such  as  s,  lying  on  the  equator,  is  in  its  daily 
motion  as  long  a  time  above  the  horizon  as  below.  If 
a  star,  such  as  s,  lies  on  the  north  side  of  the  equator,  i.e. 
on  the  side  on  which  the  north  pole  P  lies,  more  than  half 
of  its  daily  path  lies  above  the  horizon  and  less  than  half 
(as  shewn  by  the  dotted  line)  lies  below ;  and  if  a  star 
is  near  enough  to  the  north  pole  (more  precisely,  if  it  is 
nearer  to  the  north  pole  than  the  nearest  point,  K,  of  the 
horizon),  as  cr,  it  never  sets,  but  remains  continually  above 
the  horizon.  Such  a  star  is  called  a  (northern)  circumpolar 
star.  On  the  other  hand,  less  than  half  of  the  daily  path  of 
a  star  on  the  south  side  of  the  equator,  as  s',  is  above  the 
horizon,  and  a  star,  such  as  </,  the  distance  of  which  from 
the  north  pole  is  greater  than  the  distance  of  the  farthest 
point,  H,  of  the  horizon,  or  which  is  nearer  than  H  to  the 
south  pole,  remains  continually  below  the  horizon. 

10.  A  slight  ^familiarity  with  the  stars  is  enough  to  shew 
any  one  that  the  same  stars  are  not  always  visible  at  the 


FIG.  2. — The  paths  of  circumpolar  stars,  shewing  their  move- 
ment during  seven  hours.  From  a  photograph  by  Mr. 
H.  Pain.  The  thickest  line  is  the  path  of  the  pole  star. 

\_Tofacep.  8. 


§5  9,  i°]      The  Daily  Motion  of  the  Celestial  Sphere  9 

same  time  of  night.  Rather  more  careful  observation, 
carried  out  for  a  considerable  time,  is  necessary  in  order 
to  see  that  the  aspect  of  the  sky  changes  in  a  regular  way 
from  night  to  night,  and  that  after  the  lapse  of  a  year  the 
same  stars  become  again  visible  at  the  same  time.  The 
explanation  of  these  changes  as  due  to  the  motion  of 
the  sun  on  the  celestial  sphere  is  more  difficult,  and  the 


*S' 


FIG.  3.— The  circles  of  the  celestial  sphere. 

unknown  discoverer   of  this   fact  certainly  made  one   of 
the  most  important  steps  in  early  astronomy. 

If  an  observer  notices  soon  after  sunset  a  star  somewhere 
in  the  west,  and  looks  for  it  again  a  few  evenings  later  at 
about  the  same  time,  he  finds  it  lower  down  and  nearer  to 
the  sun ;  a  few  evenings  later  still  it  is  invisible,  while  its 
place  has  now  been  taken  by  some  other  star  which  was  at 
first  farther  east  in  the  sky.  This  star  can  in  turn  be 
observed  to  approach  the  sun  evening  by  evening.  Or  if 
the  stars  visible  after  sunset  low  down  in  the  east  are 


to  A  Short  History  of  Astronomy  [CH.  i. 

noticed  a  few  days  later,  they  are  found  to  be  higher  up 
in  the  sky,  and  their  place  is  taken  by  other  stars  at 
first  too  low  down  to  be  seen.  Such  observations  of 
stars  rising  or  setting  about  sunrise  or  sunset  shewed  to 
early  observers  that  the  stars  were  gradually  changing  their 
position  with  respect  to  the  sun,  or  that  the  sun  was 
changing  its  position  with  respect  to  the  stars. 

The  changes  just  described,  coupled  with  the  fact  that 
the  stars  do  not  change  their  positions  with  respect  to  one 
another,  shew  that  the  stars  as  a  whole  perform  their  daily 
revolution  rather  more  rapidly  than  the  sun,  and  at  such  a 
rate  that  they  gain  on  it  one  complete  revolution  in  the 
course  of  the  year.  This  can  be  expressed  otherwise  in 
the  form  that  the  stars  are  all  moving  westward  on  the 
celestial  sphere,  relatively  to  the  sun,  so  that  stars  on  the 
east  are  continually  approaching  and  those  on  the  west 
continually  receding  from  the  sun.  But,  again,  the  same 
facts  can  be  expressed  with  equal  accuracy  and  greater 
simplicity  if  we  regard  the  stars  as  fixed  on  the  celestial 
sphere,  and  the  sun  as  moving  on  it  from  west  to  east 
among  them  (that  is,  in  the  direction  opposite  to  that  of 
the  daily  motion),  and  at  such  a  rate  as  to  complete  a 
circuit  of  the  celestial  sphere  and  to  return  to  the  same 
position  after  a  year. 

This  annual  motion  of  the  sun  is,  however,  readily  seen 
not  to  be  merely  a  motion  from  west  to  east,  for  if  so  the 
sun  would  always  rise  and  set  at  the  same  points  of  the 
horizon,  as  a  star  does,  and  its  midday  height  in  the  sky 
and  the  time  from  sunrise  to  sunset  would  always  be  the 
same.  We  have  already  seen  that  if  a  star  lies  on  the 
equator  half  of  its  daily  path  is  above  the  horizon,  if 
the  star  is  north  of  the  equator  more  than  half,  and  if  south 
of  the  equator  less  than  half;  and  what  is  true  of  a  star  is  true 
for  the  same  reason  of  any  body  sharing  the  daily  motion  of 
the  celestial  sphere.  During  the  summer  months  therefore 
(March  to  September),  when  the  day  is  longer  than  the  night, 
and  more  than  half  of  the  sun's  daily  path  is  above  the 
horizon,  the  sun  must  be  north  of  the  equator,  and  during 
the  winter  months  (September  to  March)  the  sun  must  be 
south  of  the  equator.  The  change  in  the  sun's  distance 
from  the  pole  is  also  evident  from  the  fact  that  in  the  winter 


*  II] 


The  Annual  Motion  of  the  Sun 


ii 


NORTH    POLE 


months  the  sun  is  on  the  whole  lower  down  in  the  sky  than 
in  summer,  and  that  in  particular  its  midday  height  is  less. 

ii.  The  sun's  path  on  the  celestial  sphere  is  therefore 
oblique  to  the  equator,  lying  partly  on  one  side  of  it  and 
partly  on  the  other.  A  good  deal  of  careful  observation 
of  the  kind  we  have  been  describing  must,  however,  have 
been  necessary  before  it  was  ascertained  that  the  sun':*, 
annual  path  on  the  celestial  sphere  (see  fig.  4)  is  a  great 
circle  (that  is,  a  circle  having  its  centre  at  the  centre  of 
the  sphere).  This  great  circle  is  now  called  the  ecliptic 
(because  eclipses  take  place  only  when  the  moon  is  in 
or  near  it),  and  the  angle  at  which  it  cuts  the  equator  is 
called  the  obliquity  of  the  ecliptic.  The  Chinese  claim  to 
have  measured  the  obliquity  in  uoo  B.C.,  and  to  have  found 
the  remarkably  accurate  value  23°  52'  (cf.  chapter  n.,  §  35). 
The  truth  of  this  statement  may  reasonably  be  doubted,  but 
on  the  other  hand  the  statement  of  some  late  Greek  writers 
that  either  Pythagoras  or  Anaximander  (6th  century  B.C.)  was 
the  first  to  discover  the 
obliquity  of  the  ecliptic  is 
almost  certainly  wrong.  It 
must  have  been  known  with 
reasonable  accuracy  to  both 
Chaldaeans  and  Egyptians 
long  before. 

When  the  sun  crosses  the 
equator  the  day  is  equal  to 
the  night,  and  the  times 
when  this  occurs  are  con- 
sequently known  as  the 
equinoxes,  the  vernal  equi- 
nox occurring  when  the  sun 
crosses  the  equator  from 
south  to  north  (about  March 
2 i st),  and  the  autumnal 
equinox  when  it  crosses  back  (about  September  23rd). 
The  points  on  the  celestial  sphere  where  the  sun  crosses 
the  equator  (A,  c  in  fig.  4),  i.e.  where  ecliptic  and  equator 
cross  one  another,  are  called  the  equinoctial  points, 
occasionally  also  the  equinoxes. 

After  the  vernal  equinox  the  sun  in  its  path  along  the 


SOUTH   POLE 


FIG.  4. — The  equator  and  the 
ecliptic. 


1 1  A  Short  History  of  Astronomy  [CH.  t. 

ecliptic  recedes  from  the  equator  towards  the  north,  until  it 
reaches,  about  three  months  afterwards,  its  greatest  distance 
from  the  equator,  and  then  approaches  the  equator  again. 
The  time  when  the  sun  is  at  its  greatest  distance  from  the 
equator  on  the  north  side  is  called  the  summer  solstice, 
because  then  the  northward  motion  of  the  sun  is  arrested 
and  it  temporarily  appears  to  stand  still.  Similarly  the  sun 
is  at  its  greatest  distance  from  the  equator  towards  the 
south  at  the  winter  solstice.  The  points  on  the  ecliptic 
(B,  D  in  fig.  4)  where  the  sun  is  at  the  solstices  are  called 
the  solstitial  points,  and  are  half-way  between  the  equinoctial 
points. 

12.  The  earliest  observers  probably  noticed  particular 
groups  of  stars  remarkable  for  their  form  or  for  the  presence 
of  bright  stars  among  them,  and  occupied  their  fancy  by 
tracing  resemblances  between  them  and  familiar  objects,  etc. 
We  have  thus  at  a  very  early  period  a  rough  attempt  at 
dividing  the  stars  into  groups  called  constellations  and  at 
naming  the  latter. 

In  some  cases  the  stars  regarded  as  belonging  to  a  con- 
stellation form  a  well-marked  group  on  the  sky,  sufficiently 
separated  from  other  stars  to  be  conveniently  classed 
together,  although  the  resemblance  which  the  group  bears 
to  the  object  after  which  it  is  named  is  often  very  slight. 
The  seven  bright  stars  of  the  Great  Bear,  for  example,  form 
a  group  which  any  observer  would  very  soon  notice  and 
naturally  make  into  a  constellation,  but  the  resemblance 
to  a  bear  of  these  and  the  fainter  stars  of  the  constellation 
is  sufficiently  remote  (see  fig.  5),  and  as  a  matter  of  fact 
this  part  of  the  Bear  has  also  been  called  a  Waggon  and 
is  in  America  familiarly  known  as  the  Dipper ;  another 
constellation  has  sometimes  been  called  the  Lyre  and 
sometimes  also  the  Vulture.  In  very  many  cases  the  choice 
of  stars  seems  to  have  been  made  in  such  an  arbitrary 
manner,  as  to  suggest  that  some  fanciful  figure  was  first 
imagined  and  that  stars  were  then  selected  so  as  to  represent 
it  in  some  rough  sort  of  way.  In  fact,  as  Sir  John  Herschel 
remarks,  "  The  constellations  seem  to  have  been  purposely 
named  and  delineated  to  cause  as  much  confusion  and 
inconvenience  as  possible.  Innumerable  snakes  twine 
through  long  and  contorted  areas  of  the  heavens  where  no 


M  12, 13]  The  Constellations  :  the  Zodiac  13 

memory  can  follow  them  ;  bears,  lions,  and  fishes,  large  and 
:;mall,  confuse  all  nomenclature."  (Outlines  of  Astronomy ', 
§301.) 

The  constellations  as  we  now  have  them  are,  with  the 
exception  of  a  certain  number  (chiefly  in  the  southern 
skies)  which  have  been  added  in  modern  times,  substantially 
those  which  existed  in  early  Greek  astronomy ;  and  such 
information  as  we  possess  of  the  Chaldaean  and  Egyptian 
constellations  shews  resemblances  indicating  that  the  Greeks 
borrowed  some  of  them.  The  names,  as  far  as  they  are 
not  those  of  animals  or  common  objects  (Bear,  Serpent, 
Lyre,  etc.),  are  largely  taken  from  characters  in  the  Greek 
mythology  (Hercules,  Perseus,  Orion,  etc.).  The  con- 
stellation Berenice's  Hair,  named  after  an  Egyptian  queen 
of  the  3rd  century  B.C.,  is  one  of  the  few  which  com- 
memorate a  historical  personage.* 

13.  Among  the  constellations  which  first  received  names 
were  those  through  which  the  sun  passes  in  its  annual 
circuit  of  the  celestial  sphere,  that  is  those  through  which 
the  ecliptic  passes.  The  moon's  monthly  path  is  also  a  great 
circle,  never  differing  very  much  from  the  ecliptic,  and  the 
paths  of  the  planets  (§  14)  are  such  that  they  also  are  never 
far  from  the  ecliptic.  Consequently  the  sun,  the  moon, 
and  the  five  planets  were  always  to  be  found  within  a  region 
of  the-  sky  extending  about  8°  on  each  side  of  the  ecliptic. 
This  strip  of  the  celestial  sphere  was  called  the  zodiac,' 
.because  the  constellations  in  it  were  (with  one  exception)' 
named  after  living  things  (Greek  £o>ov,  an  animal) ;  it  was  \ 
divided  into  twelve  'equal  parts,  the  signs  of  the  zodiac, 
through  one  of  which  the  sun  passed  every  month,  so  that 
the  position  of  the  sun  at  any  time  could  be  roughly 
described  by  stating  in  what  "  sign  "  it  was.  The  stars  in 
each  "  sign  "  were  formed  into  a  constellation,  the  "  sign  " 
and  the  constellation  each  receiving  the  same  name.  Thus 

*  I  have  made  no  attempt  either  here  or  elsewhere  to  describe  the 
constellations  and  their  positions,  as  I  believe  such  verbal  descrip- 
tions to  be  almost  useless.  For  a  beginner  who  wishes  to  become 
familiar  with  them  the  best  plan  is  to  get  some  better  informed 
friend  to  point  out  a  few  of  the  more  conspicuous  ones,  in  different 
parts  of  the  sky.  Others  can  then  be  readily  added  by  means  of  a 
star-atlas,  or  of  the  star-maps  given  in  many  textbooks. 


14  A  Short  History  of  Astronomy  [CH.  I. 

arose  twelve  zodiacal  constellations,  the  names  of  which 
have  come  down  to  us  with  unimportant  changes  from 
early  Greek  times.*  Owing,  however,  to  an  alteration  of 
the  position  of  the  equator,  and  consequently  of  the 
equinoctial  points,  the  sign  Aries,  which  was  defined  by 
Hipparchus  in  the  second  century  B.C.  (see  chapter  n.,  §  42) 
as  beginning  at  the  vernal  equinoctial  point,  no  longer 
contains  the  constellation  Aries,  but  the  preceding  one, 
Pisces  ;  and  there  is  a  corresponding  change  throughout 
the  zodiac.  The  more  precise  numerical  methods  of 
modern  astronomy  have,  however,  rendered  the  signs  of 
the  zodiac  almost  obsolete ;  but  the  first  point  of  Aries  (  T  ), 
and  the  first  point  of  Libra  (=2=),  are  still  the  recognised 
names  for  the  equinoctial  points. 

In  some  cases  individual  stars  also  received  special 
names,  or  were  called  after  the  part  of  the  constellation  in 
which  they  were  situated,  e.g.  Sirius,  the  Eye  of  the  Bull, 
the  Heart  of  the  Lion,  etc.  ;  but  the  majority  of  the  present 
names  of  single  stars  are  of  Arabic  origin  (chapter  in.,  §  64). 

14.  We  have  seen  that  the  stars,  as  a  whole,  retain 
invariable  positions  on  the  celestial  sphere,t  whereas  the 
sun  and  moon  change  their  positions.  It  was,  however, 
discovered  in  prehistoric  times  that  five  bodies,  at  first 
sight  barely  distinguishable  from  the  other  stars,  also  changed 
their  places.  These  five — Mercury,  Venus,  Mars,  Jupiter, 
and  Saturn — with  the  sun  and  moon,  were  called  planets,:}: 
or  wanderers,  as  distinguished  from  the  fixed  stars. 

*  The  names,  in  the  customary  Latin  forms,  are  :  Aries,  Taurus, 
Gemini,  Cancer,  Leo,  Virgo,  Libra,  Scorpio,  Sagittarius,  Capricorn  us, 
Aquarius,  and  Pisces ;  they  are  easily  remembered  by  the  doggerel 
verses : — 

The  Ram,  the  Bull,  the  Heavenly  Twins, 
And  next  the  Crab,  the  Lion  shines, 

The  Virgin  and  the  Scales, 
The  Scorpion,  Archer,  and  He-Goat, 
The  Man  that  bears  the  Watering-pot, 

And  Fish  with  glittering  tails. 

f  This  statement  leaves  out  of  account  small  motions  nearly  or 
quite  invisible  to  the  naked  eye,  some  of  which  are  among  the  most 
interesting  discoveries  of  telescopic  astronomy ;  see,  for  example, 
chapter  x./§§  207-215. 

J  The  custom  of  calling  the  sun  and  moon  planets  has  now  died 
out,  and  the  modern  usage  will  be  adopted  henceforward  in  this 
book. 


M  14,  15]  The  Planets  \  5 

Mercury  is  never  l-fEEf*  except  occasionally  near  the  horizon 
just  after  sunset  or  before  sunrise,  and  in  a  climate  like 
ours  requires  a  good  deal  of  looking  for ;  and  it  is  rather 
remarkable  that  no  record  of  its  discovery  should  exist. 
Venus  is  conspicuous  as  the  Evening  Star  'or  as  the 
Morning  Star.  The  discovery  of  the  identity  of  the 
Evening  and  Morning  Stars  is  attributed  to  Pythagoras 
(6th  century  B.C.),  but  must  almost  certainly  have  been 
made  earlier,  though  the  Homeric  poems  contain  references 
to  both,  without  any  indication  of  their  identity.  Jupiter  is 
at  times  as  conspicuous  as  Venus  at  her  brightest,  while 
Mars  and  Saturn,  when  well  situated,  rank  with  the  brightest 
of  the  fixed  stars. 

The  paths  of  the  planets  on  the  celestial  sphere  are,  as 
we  have  seen  (§  13),  never  very  far  from  the  ecliptic ;  but 
whereas  the  sun  and  moon  move  continuously  along  their 
paths  from  west  to  east,  the  motion  of  a  planet  is  some- 
times from  west  to  east,  or  direct,  and  sometimes  from  east 
to  west,  or  retrograde.  If  we  begin  to  watch  a  planet  when 
it  is  moving  eastwards  among  the  stars,  we  find  that  after 
a  time  the  motion  becomes  slower  and  slower,  until  the 
planet  hardly  seems  to  move  at  all,  and  then  begins  to 
move  with  gradually  increasing  speed  in  the  opposite 
direction ;  after  a  time  this  westward  motion  becomes 
slower  and  then  ceases,  and  the  planet  then  begins  to  move 
eastwards  again,  at  first  slowly  and  then  faster,  until  it 
returns  to  its  original  condition,  and  the  changes  are 
repeated.  When  the  planet  is  just  reversing  its  motion  it 
is  said  to  be  stationary,  and  its  position  then  is  called  a 
stationary  point.  The  time  during  which  a  planet's  motion 
is  retrograde  is,  however,  always  considerably  less  than  that 
during  which  it  is  direct;  Jupiter's  motion,  for  example, 
is  direct  for  about  39  weeks  and  retrograde  for  17,  while 
Mercury's  direct  motion  lasts  13  or  14  weeks  and  the  retro- 
grade motion  only  about  3  weeks  (see  figs.  6,  7).  On  the 
whole  the  planets  advance  from  west  to  east  and  describe 
circuits  round  the  celestial  sphere  in  periods  which  are 
different  for  each  planet.  The  explanation  of  these  irregu- 
larities in  the  planetary  motions  was  long  one  of  the  great 
difficulties  of  astronomy. 

15.  The   idea  that  some  of  the   heavenly   bodies   are 


i6 


A  Short  History  of  Astronomy 


[Cn.  I. 


nearer  to  the  earth  than  others  must  have  been  suggested 
by  eclipses  (§  17)  and  occultations,  i.e.  passages  of  the 
moon  over  a  planet  or  fixed  star.  In  this  way  the  moon 
would  be  recognised  as  nearer  than  any  of  the  other 
celestial  bodies.  No  direct  means  being  available  for 
determining  the  distances,  rapidity  of  motion  was  employed 
as  a  test  of  probable  nearness.  Now  Saturn  returns  to  the 
same  place  among  the  stars  in  about  29^  years,  Jupiter  in 
12  years,  Mars  in  2  years,  the  sun  in  one  year,  Venus  in  225 


April 


May  14 


May 


July  I 


Mar.  19 


July  15 


s°s. 


FIG.  6. — The  apparent  path  of  Jupiter  from  Oct.  28,  1897,  to 
Sept.  3,  1898.  The  dates  printed  in  the  diagram  shew  the 
positions  of  Jupiter.  « 

days,  Mercury  in  88  days,  and  the  moon  in  27  days;  and 
this  order  was  usually  taken  to  be  the  order  of  distance, 
Saturn  being  the  most  distant,  the  moon  the  nearest.  The 
stars  being  seen  above  us  it  was  natural  to  think  of  the 
most  distant  celestial  bodies  as  being  the  highest,  and 
accordingly  Saturn,  Jupiter,  and  Mars  being  beyond  the 
sun  were  called  superior  planets,  as  distinguished  from  the' 
two  inferior  planets  Venus  and  Mercury.  This  division 
corresponds  also  to  a  difference  in  the  observed  motions, 
as  Venus  and  Mercury  seem  to  accompany  the  sun  in  its 


16] 


The  Measurement  of  Time 


annual  journey,  being  never  more  than  about  47  and  29° 
respectively  distant  from  it,  on  either  side  ;  while  the  other 
planets  are  not  thus  restricted  in  their  motions. 

1 6.  One  of  the  purposes  to  which  applications  of 
astronomical  knowledge  was  first  applied  was  to  the 
measurement  of  time.  As  the  alternate  appearance  and 
disappearance  of  the  sun,  bringing  with  it  light  and  heat, 
is  the  most  obvious  of  astronomical  facts,  so  the  day  is 


FIG.  '/.— The  apparent  path  of  Mercury  from  Aug.  I  to  Oct.  3, 
1898.  The  dates  printed  in  capital  letters  shew  the  positions 
of  the  sun  ;  the  other  dates  shew  those  of  Mercury. 

the  simplest  unit  of  time.*  Some  of  the  early  civilised 
nations  divided  the  time  from  sunrise  to  sunset  and  also 
the  night  each  into  12  equal  hours.  According  to  this 
arrangement  a  day-hour  was  in  summer  longer  than  a 

*  It  maybe  noted  that  our  word  "day"  (and  the  corresponding 
word  in  other  languages)  is  commonly  used  in  two  senses,  either  for 
the  time  between  sunrise  and  sunset  (day  as  distinguished  from 
night),  or  for  the  whole  period  of  24  hours  or  day-and-night.  The 
Greeks,  however,  used  for  the  latter  a  special  word, 


1 8  A  Short  History  of  Astronomy  [CH.  i. 

night-hour  and  in  winter  shorter,  and  the  length  of  an  hour 
varied  during  the  year.  At  Babylon,  for  example,  where 
this  arrangement  existed,  the  length  of  a  day-hour  was  at 
midsummer  about  half  as  long  again  as  in  midwinter,  and 
in  London  it  would  be  about  twice  as  long.  It  was  there- 
fore a  great  improvement  when  the  Greeks,  in  comparatively 
late  times,  divided  the  whole  day  into  24  equal  hours. 
Other  early  nations  divided  the  same  period  into  1 2  double 
hours,  and  others  again  into  60  hours. 

The  next  most  obvious  unit  of  time  is  the  lunar  month, 
or  period  during  which  the  moon  goes  through  her  phases. 
A  third  independent  unit  is  the  year.  Although  the  year 
is  for  ordinary  life  much  more  important  than  the  month, 
yet  as  it  is  much  longer  and  any  one  time  of  year  is  harder 
to  recognise  than  a  particular  phase  of  the  moon,  the  length 
of  the  year  is  more  difficult  to  determine,  and  the  earliest 
known  systems  of  time-measurement  were  accordingly 
based  on  the  month,  not  on  the  year.  The  month  was 
found  to  be  nearly  equal  to  29^  days,  and  as  a  period 
consisting  of  an  exact  number  of  days  was  obviously  con- 
venient for  most  ordinary  purposes,  months  of  29  or  30 
days  were  used,  and  subsequently  the  calendar  was  brought 
into  closer  accord  with  the  moon  by  the  use  of  months 
containing  alternately  29  and  30  days  (cf.  chapter  n.,  §  19). 

Both  Chaldaeans  and  Egyptians  appear  to  have  known 
that  the  year  consisted  of  about  365^  days;  and  the  latter, 
for  whom  the  importance  of  the  year  was  emphasised  by 
the  rising  and  falling  of  the  Nile,  were  probably  the  first 
nation  to  use  the  year  in  preference  to  the  month  as  a 
measure  of  time.  They  chose  a  year  of  365  days. 

The  origin  of  the  week  is  quite  different  from  that  of 
the  month  or  year,  and  rests  on  certain  astrological  ideas 
about  the  planets.  To  each  hour  of  the  day  one  of  the 
seven  planets  (sun  and  moon  included)  was  assigned  as  a 
"  ruler,"  and  each  day  named  after  the  planet  which  ruled 
its  first  hour.  The  planets  being  taken  in  the  order 
already  given  (§  15),  Saturn  ruled  the  first  hour  of  the 
first  day,  and  therefore  also  the  8th,  i5th,  and  22nd  hours 
of  the  first  day,  the  5th,  i2th,  and  igth  of  the  second  day, 
and  so  on;  Jupiter  ruled  the  2nd,  gth,  i6th,  and  23rd 
hours  of  the  first  day,  and  subsequently  the  ist  hour  of 


§  ij]  The  Measurement  of  Time:  Eclipses  19 

the  6th  day.  In  this  way  the  first  hours  of  successive 
days  fell  respectively  to  Saturn,  the  Sun,  the  Moon,  Mars, 
Mercury,  Jupiter,  and  Venus.  The  first  three  are  easily 
recognised  in  our  Saturday,  Sunday,  and  Monday  ;  in  the 
other  days  the  names  of  the  Roman  gods  have  been 
replaced  by  their  supposed  Teutonic  equivalents — Mercury 
by  Wodan,  Mars  by  Thues,  Jupiter  by  Thor,  Venus  by 
Freia.* 

17.  Eclipses  of  the  sun  and  moon  must  from  very  early 
times  have  excited  great  interest,  mingled  with  superstitious 
terror,  and  the  hope  of  acquiring  some  knowledge  of  them 
was  probably  an  important  stimulus  to  early  astronomical 
work.  That  eclipses  of  the  sun  only  take  place  at  new 
moon,  and  those  of  the  moon  only  at  full  moon,  must  have 
been  noticed  after  very  little  observation  ;  that  eclipses  of 
the  sun  are  caused  by  the  passage  of  the  moon  in  front 
of  it  must  have  been  only  a  little  less  obvious ;  but  the 
discovery  that  eclipses  of  the  moon  are  caused  by  the 
earth's  shadow  was  probably  made  much  later.  In  fact 
even  in  the  time  of  Anaxagoras  (5th  century  B.C.)  the  idea 
was  so  unfamiliar  to  the  Athenian  public  as  to  be  regarded 
as  blasphemous. 

One  of  the  most  remarkable  of  the  Chaldaean  con-  \ 
tributions  to  astronomy  was  the  discovery  (made  at  any 
rate  several  centuries  B.C.)  of  the  recurrence  of  eclipses 
after  a  period,  known  as  the  saros,  consisting  of  6,585  days 
(or  eighteen  of  our  years  and  ten  or  eleven  days,,  according 
as  five  or  four  leap-years  are  included).  It  is  probable 
that  the  discovery  was  made,  not  by  calculations  based  on 
knowledge  of  the  motions  of  the  sun  and  moon,  but  by 
mere  study  of  the  dates  on  which  eclipses  were  recorded 
to  have  taken  place.  As,  however,  an  eclipse  of  the  sun 
(unlike  an  eclipse  of  the  moon)  is  only  visible  over  a  small 
part  of  the  surface  of  the  earth,  and  eclipses  of  the  sun 
occurring  at  intervals  of  eighteen  years  are  not  generally 
visible  at  the  same  place,  it  is  not  at  all  easy  to  see  how 
the  Chaldaeans  could  have  established  their  cycle  for  this 
case,  nor  is  it  in  fact  clear  that  the  saros  was  supposed  to 
apply  to  solar  as  well  as  to  lunar  eclipses.  The  saros  may 

*  Compare  the  French  :  Mardi,  Mercredi,  Jeudi,  Vendredi ;  or 
better  still  the  Italian  :  Marled i,  Mcrcoledi,  Giovedi,  Venerdi. 


20  A  Short  History  of  Astronomy         [CH.  i.,  §  18 

be  illustrated  in  modern  times  by  the  eclipses  of  the  sun 
which  took  place  on  July  i8th,  1860,  on  July  29th,  1878, 
and  on  August  9th,  1896;  but  the  first  was  visible  in 
Southern  Europe,  the  second  in  North  America,  and  the 
third  in  Northern  Europe  and  Asia. 

1 8.  To  the  Chaldaeans  may  be  assigned  also  the  doubtful 
honour  of  having  been  among  the  first  to  develop  astrology, 
the  false  science  which  has  professed  to  ascertain  the  in- 
fluence of  the  stars  on  human  affairs,  to  predict  by  celestial 
observations  wars,  famines,  and  pestilences,  and  to  discover 
the  fate  of  individuals  from  the  positions  of  the  stars  at 
their  birth.  A  belief  in  some  form  of  astrology  has  always 
prevailed  in  oriental  countries ;  it  flourished  at  times  among 
the  Greeks  and  the  Romans ;  it  formed  an  important  part 
of  the  thought  of  the  Middle  Ages,  and  -«— net  even  quite 
extinct  among  ourselves  at  the  present  day.*  It  should, 
however,  be  remembered  that  if  the  history  of  astrology  is 
a  painful  one,  owing  to  the  numerous  illustrations  which 
it  affords  of  human  credulity  and  knavery,  the  belief  in 
it  has  undoubtedly  been  a  powerful  stimulus  to  genuine 
astronomical  study  (cf.  chapter  in.,  §  56,  and  chapter  v., 

§§  99>  I0°)- 

*  See,  for  example,  Old  Moore's  or  Zadkiels  Almanack. 


CHAPTER   II. 

GREEK    ASTRONOMY. 

"  The  astronomer  discovers  that  geometry,  a  pure  abstraction  of  the 
human  mind,  is  the  measure  of  planetary  motion." 

EMERSON. 

19.  IN  the  earlier  period  of  Greek  history  one  of  the 
chief  functions  expected  of  astronomers  was  the  proper 
regulation  of  the  calendar.  The  Greeks,  like  earlier 
nations,  began  with  a  calendar  based  on  the  moon.  In 
the  time  of  Hesiod  a  year  consisting  of  12  months  of  30 
days  was  in  common  use  ;  at  a  later  date  a  year  made  up 
of  6  full  months  of  30  days  and  6  empty  months  of  29  days 
was  introduced.  To  Solon  is  attributed  the  merit  of 
having  introduced  at  Athens,  about  594  B.C.,  the  practice 
of  adding  to  every  alternate  year  a  "  full  "  month.  Thus  a 
period  of  two  years  would  contain  13  months  of  30  days 
and  12  of  29  days,  or  738  days  in  all,  distributed  among 
25  months,  giving,  for  the  average  length  of  the  year  and 
month,  369  days  and  about  29 J  days  respectively.  This 
arrangement  was  further  improved  by  the  introduction, 
probably  during  the  5th  century  B.C.,  of  the  octaeteris,  or 
eight-year  cycle,  in  three  of  the  years  of  which  an  additional 
"full"  month  was  introduced,  while  the  remaining  years 
consisted  as  before  of  6  "  full "  and  6  "  empty "  months. 
By  this  arrangement  the  average  length  of  the  year  was 
reduced  to  365!  days,  that  of  the  month  remaining  nearly 
unchanged.  As,  however,  the  Greeks  laid  some  stress  on 
beginning  the  month  when  the  new  moon  was  first  visible, 
it  was  necessary  to  make  from  time  to  time  arbitrary 
alterations  in  the  calendar,  and  considerable  confusion 


22  A  Short  History  of  Astronomy  [CH.  il. 

resulted,  of  which  Aristophanes  makes  the  Moon  complain 
in  his  play  The  Clouds ;  acted  in  423  B.C.  : 

"  Yet  you  will  not  mark  your  days 

As  she  bids  you,  but  confuse  them,  jumbling  them  all  sorts  of  ways. 
And,  she  says,  the  Gods  in  chorus  shower  reproaches  on  her  head, 
When,  in  bitter  disappointment,  they  go  supperless  to  bed, 
Not  obtaining  festal  banquets,  duly  on  the  festal  day." 

20.  A  little   later,  the   astronomer   Meton   (born   about 
460  B.C.)  made  the  discovery  that  the  length  of  19  years 
is   very   nearly   equal   to   that  of  235   lunar  months   (the 
difference  being  in  fact  less  than  a  day),  and  he  devised 
accordingly  an  arrangement  of  12  years  of  12  months  and 
7   of  13  months,   125   of  the  months  in  the  whole  cycle 
being  "full"  and  the  others  "empty."     Nearly  a  century 
later  Callippus  made  a  slight  improvement,  by  substituting 
in  every  fourth  period  of  19  years  a  "full"  month  for  one  of 
the  "  empty  "  ones.    Whether  Meton's  cycle,  as  it  is  called, 
was  introduced  for  the  civil  calendar  or  not  is  uncertain, 
but  if  not  it  was  used  as  a  standard  by  reference  to  which 
the  actual  calendar  was  from  time  to  time  adjusted.     The 
use  of  this  cycle  seems  to  have  soon  spread  to  other  parts 
of  Greece,  and  it  is  the  basis  of  the  present  ecclesiastical 
rule  for  fixing  Easter.    The  difficulty  of  ensuring  satisfactory 
correspondence  between  the  civil  calendar  and  the  actual 
motions  of  the  sun  and  moon  led  to  the  practice  of  publish- 
ing from   time   to  time  tables   (TrapaTnJy/xara)  not  unlike 
our  modern  almanacks,  giving  for   a   series   of  years  the 
dates  of  the  phases  of  the  moon,  and  the  rising  and  setting 
of  some  of  the  fixed  stars,  together  with  predictions  of  the 
weather.     Owing  to  the  same  cause  the  early  writers  on 
agriculture  (e.g.   Hesiod)  fixed   the   dates   for  agricultural 
operations,  not  by  the  calendar,  but  by  the  times  of  the 
rising   and  setting  of  constellations,  i.e.  the   times   when 
they  first  became  visible  before  sunrise  orV^rp  last  visible 
immediately  after  sunset — a  practice  which  was  continued 
long  after  the  establishment  of  a  fairly  satisfactory  calendar, 
and  was  apparently  by  no  means  extinct  in  the  time  of 
Galen  (2nd  century  A.D.). 

21.  The  Roman  calendar  was  in  early  times  even  more 
confused  than  the  Greek.     There  appears  to  have  been 


$§2o—22]  The    Greek  and  Roman   Calendars  23 

at  one  time  a  year  of  either  304  or  354  days ;  tradition 
assigned  to  Numa  the  introduction  of  a  cycle  of  four  years, 
which  brought  the  calendar  into  fair  agreement  with  the 
sun,  but  made  the  average  length  of  the  month  consider- 
ably too  short.  Instead,  however,  of  introducing  further 
refinements  the  Romans  cut  the  knot  by  entrusting  to 
the  ecclesiastical  authorities  the  adjustment  of  the 
calendar  from  time  to  time,  so  as  to  make  it  agree  with 
the  sun  and  moon.  According  to  one  account,  the 
first  day  of  each  month  was  proclaimed  by  a  crier. 
Owing  either  to  ignorance,  or,  as  was  alleged,  to  politi- 
cal and  commercial  favouritism,  the  priests  allowed  the 
calendar  to  fall  into  a  state  of  great  confusion,  so  that, 
as  Voltaire  remarked,  "  les  generaux  remains  triomphaient 
toujours,  mais  ils  ne  savaient  pas  quel  jour  ils  triom- 
phaient." 

A  satisfactory  reform  of  the  calendar  was  finally  effected 
by  Julius  Caesar  during  the  short  period  of  his  supremacy 
at  Rome,  under  the  advice  of  an  Alexandrine  astronomer 
Sosigenes.  The  error  in  the  calendar  had  mounted  up 
to  such  an  extent,  that  it  was  found  necessary,  in  order 
to  correct  it,  to  interpolate  three  additional  months  in 
a  single  year  (46  B.C.),  bringing  the  total  number  of  days 
in  that  year  up  to  445.  For  the  future  the  year  was  to 
be  independent  of  the  moon ;  the  ordinary  year  was 
to  consist  of  365  days,  an  extra  day  being  added  to  Feb- 
ruary every  fourth  year  (our  leap-year),  so  that  the  average 
length  of  the  year  would  be  3655  days. 

The  new  system  began  with  the  year  45  B.C.,  and  soon 
spread,  under  the  name  of  the  Julian  Calendar,  over  the 
civilised  world. 

22.  To  avoid  returning  to  the  subject,  it  may  be  con- 
venient to  deal  here  with  the'  only  later  reform  of  any 
importance. 

The  difference  between  the  average  length  of  the 
year  as  fixed  by  Julius  Caesar  and  the  true  year  is  so 
small  as  only  to  amount  to  about  one  day  in  128  years.  By 
the  latter  half  of  the  i6th  century  the  date  of  the  vernal 
equinox  was  therefore  about  ten  days  earlier  than  it  was 
at  the  time  of  the  Council  of  Nice  (A.D.  325),  at  which 
rules  for  the  observance  of  Easter  had  been  fixed.  Pope 


24  A  Short  History  of  Astronomy  [CH.  n. 

Gregory  XIII.  introduced  therefore,  in  1582,  a  slight  change; 
ten  days  were  omitted  from  that  year,  and  it  was  arranged 
to  omit  for  the  future  three  leap-years  in  four  centuries 
(viz.  in  1700,  1800,  1900,  2100,  etc.,  the  years  1600,  2000, 
2400,  etc.,  remaining^leap-years).  The  Gregorian  Calendar, 
or  New  Style,  as  it  was  commonly  called,  was  not  adopted 
in  England  till  1752,  when  ir  days  had  to  be  omitted; 
and  has  not  yet  been  adopted  in  Russia  and  Greece, 
the  dates  there  being  now  12  days  behind  those  of 
Western  Europe. 

23.  While  their  oriental  predecessors  had  confined 
themselves  chiefly  to  astronomical  observations,  the  earlier 
Greek  philosophers  appear  to  have  made  next  to  no 
observations  of  importance,  and  to  have  been  far  more 
interested  in  inquiring  into  causes  of  phenomena.  Thales, 
the  founder  of  the  Ionian  school,  was  credited  by  later 
writers  with  the  introduction  of  Egyptian  astronomy  into 
Greece,  at  about  the  end  of  the  7th  century  B.C.  ;  but  both 
Thales  and  the  majority  of  his  immediate  successors  appear 
to  have  added  little  or  nothing  to  astronomy,  except  some 
rather  vague  speculations  as  to  the  form  of  the  earth 
and  its  relation  to  the  rest  of  the  world.  On  the  other 
hand,  some  real  progress  seems  to  have  been  made  by 
Pythagoras*  and  his  followers.  Pythagoras  taught  that 
(~  the  earth,  in  common  with  the  heavenly  bodies,  is  a  sphere, 
and  that  it  rests  without  requiring  support  in  the  middle 
of  the  universe.  Whether  he  had  any  real  evidence  in 
support  of  these  views  is  doubtful,  but  it  is  at  any  rate 
a  reasonable  conjecture  that  he  knew  the  moon  to  be 
bright  because  the  sun  shines  on  it,  and  the  phases  to 
be  caused  by  the  greater  or  less  amount  of  the  illuminated 
half  turned  towards  us ;  and  the  curved  form  of  the 
boundary  between  the  bright  and  dark  portions  of  the 
moon  was  correctly  interpreted  by  him  as  evidence  that 
the  moon  was  spherical,  and  not  a  flat  disc,  as  it  appears 
'at  first  sight.  Analogy  would  then  probably  suggest  that  the 
earth  also  was  spherical.  However  this  may  be,  the  belief 
in  the  spherical  form  of  the  earth  never  disappeared  from 

*  We  have  little  definite  knowledge  of  his  life.  He  was  born  in 
the  earlier  part  of  the  6th  century  B.C.,  and  died  at  the  end  of  the 
jjamejcentury  or  beginning  of  the  next. 


$$  23,  24]  The  Pythagoreans  25 

Greek  thought,  and  was  in  later  times  an  established  part 
of  Greek  systems,  whence  it  has  been  handed  down, 
almost  unchanged,  to  modern  times.  This  belief  is  thus 
2,000  years  older  than  the  belief  in  the  rotation  of 
the  earth  and  its  revolution  round  the  sun  (chapter  iv.), 
doctrines  which  we  are  sometimes  inclined  to  couple  with 
it  as  the  foundations  of  modern  astronomy. 

In  Pythagoras  occurs  also,  perhaps  for  the  first  time,  an 
idea  which  had  an  extremely  important  influence  on  ancient 
and  mediaeval  astronomy.  Not  only  were  the  stars  supposed 
to  be  attached  to  a  crystal  sphere,  which  revolved  daily 
on  an  axis  through  the  earth,  but  each  of  the  seven 
planets  (the  sun  and  moon  being  included)  moved  on  a 
sphere  of  its  own.  J"he  distances  of  these  spheres  from 
the  earth  were  fixed  in  accordance  with  certain  speculative 
notions  of  Pythagoras  as  to  numbers  and  music  ;  hence 
the  spheres  as  they  revolved  produced  harmonious  sounds 
which  specially  gifted  persons  might  at  times  hear :  this 
Is  "trie  origin  of  the  idea  of  the  music  of  the  spheres  which 
recurs  continually  in  mediaeval  speculation  and  is  found 
occasionally  in  modern  literature.  At  a  later  stage  these 
spheres  of  Pythagoras  were  developed  into  a  scientific 
representation  of  the  motions  of  the  celestial  bodies,  which 
remained  the  basis  of  astronomy  till  the  time  of  Kepler 
(chapter  vii.). 

24.  The  Pythagorean  Philolaus,  who  lived  about  a 
century  later  than  his  master,  introduced  for  the  first  time 
the  idea  of  the  motion  of  the  earth  :  he  appears  to  have 
regarded  the  earth,  as  well  as  the  sun,  moon,  and  five 
planets,  as  revolving  round  some  central  fire,  the  earth 
rotating  on  its  own  axis  as  it  revolved,  apparently  in  order 
to  ensure  that  the  central  fire  should  always  remain  in- 
visible to  the  inhabitants  of  the  known  parts  of  the  earth. 
That  the  scheme  was  a  purely  fanciful  one,  and  entirely 
different  from  the  modern  doctrine  of  the  motion  of  the 
earth,  with  which  later  writers  confused  it,  is  sufficiently 
shewn  by  the  invention  as  part  of  the  scheme  of  a  purely 
imaginary  body,  the  counter-earth  (w-riyQuv),  which  brought 
the  number  of  moving  bodies  up  to  ten,  a  sacred  Pytha- 
gorean number.  The  suggestion  of  such  an  important 
idea  as  that  of  the  motion  of  the  earth,  an  idea  so 


26  A  Short  History  of  Astronomy  [Cn.  II. 

repugnant  to  uninstructed  common  sense,  although  presented 
in  such  a  crude  form,  without  any  of  the  evidence  required 
to  win  general  assent,  was,  however,  undoubtedly  a  valuable 
contribution  to  astronomical  thought.  It  is  well  worth 
notice  that  Coppernicus  in  the  great  book  which  is  the 
foundation  of  modern  astronomy  (chapter  iv.,  §  75)  especi- 
ally quotes  Philolaus  and  other  Pythagoreans  as  authorities 
for  his  doctrine  of  the  motion  of  the  earth. 

Three  other  Pythagoreans,  belonging  to  the  end  of 
the  6th  century  and  to  the  5th  century  B.C.,  Hicetas  of 
Syracuse,  Heraditus,  and  Ecphantus,  are  explicitly  mentioned 
by  later  writers  as  having  believed  in  the  rotation  of  the 
earth. 

An  obscure  passage  in  one  of  Plato's  dialogues  (the 
Timaeus)  has  been  interpreted  by  many  ancient  and  modern 
commentators  as  implying  a  belief  in  the  rotation  of  the 
earth,  and  Plutarch  also  tells  us,  partly  on  the  authority 
\  of  Theophrastus,  that  Plato  in  old  age  adopted  the  belief 
that  the  centre  of  the  universe  was  not  occupied  by  the 
earth  but  by  some  better  body.* 

Almost  the  only  scientific  Greek  astronomer  who  believed 
in  the  motion  of  the  earth  was  Aristarchus  of  Samos,  who 
lived  in  the  first  half  of  the  3rd  century  B.C.,  and  is  best 
known  by  his  measurements  of  the  distances  of  the  sun 
and  moon  (§  32).  He  held  that  the  sun  and  fixed  stars 
were  motionless,  the  sun  being  in  the  centre  of  the  sphere 
on  which  the  latter  lay,  and  that  the  earth  not  only  rotated 
on  its  axis,  but  also  described  an  orbit  round  the  sun. 
Seleucus  of  Seleucia,  who  belonged  to  the  middle  of  the 
2nd  century  B.C.,  also  held  a  similar  opinion.  Unfor- 
tunately we  know  nothing  of  the  grounds  of  this  belief  in 
either  case,  and  their  views  appear  to  have  found  little 
favour  among  their  contemporaries  or  successors. 

It  may  also  be  mentioned  in  this  connection  that  Aristotle 
(§  27)  clearly  realised  that  the  apparent  daily  motion  of  the 
stars  could  be  explained  by  a  motion  either  Of  the  stars  or 
of  the  earth,  but  that  he  rejected  the  latter  explanation. 

25.  Plato  (about  428-347  B.C.)  devoted  no  dialogue 
especially  to  astronomy,  but  made  a  good  many  references 

*  Theophrastus  was  born  about  half  a  century,  Plutarch  nearly 
five  centuries,  later  than  Plato. 


*§  as,  a6]  Aristarchus :  Plato  27 

to  the  subject  in  various  places.  He  condemned  any 
careful  study  of  the  actual  celestial  motions  as  degrading 
rather  than  elevating,  and  apparently  regarded  the  subject 
as  worthy  of  attention  chiefly  on  account  of  its  connection 
with  geometry,  and  because  the  actual  celestial  motions 
suggested  ideal  motions  of  greater  beauty  and  interest. 
This  view  of  astronomy  he  contrasts  with  the  popular 
conception,  according  to  which  the  subject  was  useful 
chiefly  for  giving  to  the  agriculturist,  the  navigator,  and 
ethers  a  knowledge  of  times  and  seasons.*  At  the  end 
of  the  same  dialogue  he  gives  a  short  account  of  the 
celestial  bodies,  according  to  which  the  sun,  moon,  planets, 
and  fixed  stars  revolve  on  eight  concentric  and  closely 
fitting  wheels  or  circles  round  an  axis  passing  through  the 
earth.  Beginning  with  the  body  nearest  to  the  earth,  the 
order  is  Moon,  Sun,  Mercury,  Venus,  Mars,  Jupiter,  Saturn, 
stars.  The  Sun,  Mercury,  and  Venus  are  said  to  perform 
their  revolutions  in  the  same  time,  while  the  other  planets 
move  more  slowly,  statements  which  shew  that  Plato  was  at 
any  rate  aware  that  the  motions  of  Venus  and  Mercury  are 
different  from  those  of  the  other  planets.  He  also  states 
that  the  moon  shines  by  reflected  light  received  from 
the  sun. 

Plato  is  said  to  have  suggested  to  his  pupils  as  a  worthy 
problem  the  explanation  of  the  celestial  motions  by  means 
of  a  combination  of  uniform  circular  or  spherical  motions. 
Anything  like  an  accurate  theory  of  the  celestial  motions, 
agreeing  with  actual  observation,  such  as  Hipparchus  and 
Ptolemy  afterwards  constructed  with  fair  success,  would 
hardly  seem  to  be  in  accordance  with  Plato's  ideas  of  the 
true  astronomy,  but  he  may  well  have  wished  to  see 
established  some  simple  and  harmonious  geometrical 
scheme  which  would  not  be  altogether  at  variance  with 
known  facts. 

26.  Acting  to  some  extent  on  this  idea  of  Plato's,  Eudoxus 
of  Cnidus  (about  409-356  B.C.)  attempted  to  explain  the 
most  obvious  peculiarities  of  the  celestial  motions  by  means 
of  a  combination  of  uniform  circular  motions.  He  may  be 
regarded  as  representative  of  the  transition  from  speculative. 

*  Republic,  VII.  529,  530. 


28  A  Short  History  of  Astronomy  [Cn.  u. 

to  scientific  Greek  astronomy.  As  in  the  schemes  of 
several  of  his  predecessors,  the  fixed  stars  lie  on  a  sphere 
which  revolves  daily  about  an  axis  through  the  earth  ;  the 
motion  of  each  of  the  other  bodies  is  produced  by  a  com- 
bination of  other  spheres,  the  centre  of  each  sphere  lying 
on  the  surface  of  the  preceding  one.  For  the  sun  and 
moon  three  spheres  were  in  each  case  necessary  :  one  to 
produce  the  daily  motion,  shared  by  all  the  celestial 
bodies  ;  one  to  produce  the  annual  or  monthly  motion  in 
the  opposite  direction  along  the  ecliptic ;  and  a  third,  with 
its  axis  inclined  to  the  axis  of  the  preceding,  to  produce 
the  smaller  motion  to  and  from  the  ecliptic.  F^udoxus 
evidently  was  well  aware  that  the  moon's  path  is  not 
coincident  with  the  ecliptic,  and  even  that  its  path  is  not 
always  the  same,  but  changes  continuously,  so  that  the  third 
sphere  was  in  this  case  necessary ;  on  the  other  hand,  he 
could  not  possibly  have  been  acquainted  with  the  minute 
deviations  of  the  sun  from  the  ecliptic  with  which  modern 
astronomy  deals.  Either  therefore  he  used  erroneous 
observations,  or,  as  is  more  probable,  the  sun's  third  sphere 
was  introduced  to  explain  a  purely  imaginary  motion  con- 
jectured to  exist  by  "analogy"  with  the  known  motion  of 
the  moon.  For  each  of  the  five  planets  four  spheres  were 
necessary,  the  additional  one  serving  to  produce  the  variations 
in  the  speed  of  the  motion  and  the  reversal  of  the  direction  of 
motion  along  the  ecliptic  (chapter  i.,  §  14,  and  below,  §  51). 
Thus  the  celestial  motions  were  to  some  extent  explained 
by  means  of  a  system  of  27  spheres,  i  for  the  stars,  6  for 
the  sun  and  moon,  20  for  the  planets.  There  is  no  clear 
evidence  that  Eudoxus  made  any  serious  attempt  to  arrange 
either  the  size  or  the  time  of  revolution  of  the  spheres  so  as 
to  produce  any  precise  agreement  with  the  observed  motions 
of  the  celestial  bodies,  though  he  knew  with  considerable 
accuracy  the  time  required  by  each  planet  to  return  to  the 
same  position  with  respect  to  the  sun ;  in  other  words,  his 
scheme  represented  the  celestial  motions  qualitatively  but 
not  quantitatively.  On  the  other  hand,  there  is  no  reason 
to  suppose  that  Eudoxus  regarded  his  spheres  (with  the 
possible  exception  of  the  sphere  of  the  fixed  stars)  as 
material ;  his  known  devotion  to  mathematics  renders  it 
probable  that  in  his  eyes  (as  in  those  of  most  of  the 


$$  27,  28]  Eudoxus :  Aristotle  29 

scientific  Greek  astronomers  who  succeeded  him)  the 
spheres  were  mere  geometrical  figures,  useful  as  a  means 
of  resolving  highly  complicated  motions  into  simpler 
elements.  Eudoxus  was  also  the  first  Greek  recorded  to 
have  had  an  observatory,  which  was  at  Cnidus,  but  we  have 
few  details  as  to  the  instruments  used  or  as  to  the  observa- 
tions made.  We  owe,  however,  to  him  the  first  systematic 
description  of  the  constellations  (see  below,  §  42),  though 
it  was  probably  based,  to  a  large  extent,  on  rough  observa- 
tions borrowed  from  his  Greek  predecessors  or  from  the 
Egyptians.  He  was  also  an  accomplished  mathematician, 
and  skilled  in  various  other  branches  of  learning. 

Shortly  afterwards  Callippus  (§  20)  further  developed 
Eudoxus's  scheme  of  revolving  spheres  by  adding,  for 
reasons  not  known  to  us,  two  spheres  each  for  the  sun 
and  moon  and  one  each  for  Venus,  Mercury,  and  Mars, 
thus  bringing  the  total  number  up  to  34. 

27.  We  have  a  tolerably  full  account  of  the  astronomical 
views  of  Aristotle  (384-322  B.C.),  both  by  means  of  inci- 
dental references,  and  by  two  treatises — the  Meteorologica 
and  the  De  Coelo — though  another  book  of  his,  dealing 
specially  with  the  subject,  has  unfortunately  been  lost.     He 
adopted  the  planetary  scheme  of  Eudoxus  and  Callippus, 
but  imagined  on  "  metaphysical  grounds  "  that  the  spheres 
would  have  certain  disturbing  effects  on  one  another,  and 
to   counteract   these   found   it  necessary   to  add   22   fresh 
spheres,  making  56  in  all.     At  the  same  time  he  treated  the 
spheres  as  material  bodies,  thus  converting  an  ingenious  and 
beautiful  geometrical  scheme  into  a  confused  mechanism.* 
Aristotle's    spheres   were,    however,   not   adopted   by  the 
leading  Greek  astronomers  who  succeeded  him,  the  systems 
of  Hipparchus   and   Ptolemy  being   geometrical  schemes 
based  on  ideas  more  like  those  of  Eudoxus. 

28.  Aristotle,  in  common  with  other  philosophers  of  his 
time,  believed  the  heavens  and  the  heavenly  bodies  to  be 
spherical.     In  the  case  of  the  moon  he  supports  this  belief 
by  the  argument  attributed  to  Pythagoras  (§  23),  namely 
that  the  observed  appearances  of  the  moon  in  its  several 

*  Confused,  because  the  mechanical  knowledge  of  the  time  was 
quite  unequal  to  giving  any  explanation  of  the  way  in  which  these 
spheres  acted  on  one  another. 


A  Short  History  of  Astronomy 


[CH.    II. 


phases  are  those  which  would  be  assumed  by  a  spherical 
body  of  which  one  half  only  is  illuminated  by  the  sun. 
Thus  the  visible  portion  of  the  moon  is  bounded  by  two 
planes  passing  nearly  through  its  centre,  perpendicular 
respectively  to  the  lines  joining  the  centre  of  the  moon  to 
those  of  the  sun  and  earth.  In  the  accompanying  diagram, 
which  represents  a  section  through  the  centres  of  the  sun 


FIG.  8. — The  phases  of  the  moon. 


(s),  earth  (E),  and  moon  (M),  A  B  c  D  representing  on  a 
much  enlarged  scale  a  section  of  the  moon  itself,  the 
portion  DAB  which  is  turned  away  from  the  sun  is  dark, 
while  the  portion  ADC,  being  turned  away  from  the 
observer  on  the  earth,  is  in  any  case  invisible  to  him.  The 
part  of  the  moon  which  appears  bright  is  therefore  that  of 
which  B  c  is  a  section,  or  the  portion 
represented  by  F  B  G  c  in  fig.  9  (which 
represents  the  complete  moon),  which 
consequently  appears  to  the  eye  as 
bounded  by  a  semicircle  F  c  G,  and  a 
portion  F  B  G  of  an  oval  curve  (actually 
an  ellipse).  The  breadth  of  this  bright 
surface  clearly  varies  with  the  relative 
positions  of  sun,  moon,  and  earth  ;  so 
that  in  the  course  of  a  month,  during 
which  the  moon  assumes  successively  the  positions  relative 
to  sun  and  earth  represented  by  i,  2,  3,  4,  5,  6,  7,  8  in 
fig.  10,  its  appearances  are  those  represented  by  the  cor- 
responding numbers  in  fig.  n,  the  moon  thus  passing 


FIG.  9.— The  phases 
of  the  moon. 


§  29]  Aristotle :  the  Phases  of  the  Moon  3 1 

through  the  familiar  phases  of  crescent,  half  full,  gibbous, 
full  moon,  and  gibbous,  half  full,  crescent  again.* 


€ 


DIRECTION 


1   OF  THE  SUN 


7 
FIG.  10. — The  phases  of  the  moon. 

Aristotle  then  argues  that  as  one  heavenly  body  is 
spherical,  the  others  must  be  so  also,  and  supports  this 
conclusion  by  another  argument,  equally  inconclusive  to 

•COOO3O 

12345678 

FIG.  II. — The  phases  of  the  mcon. 

us,  that  a  spherical  form  is  appropriate  to  bodies  moving  as 
the  heavenly  bodies  appear  to  do. 

29.  His  proofs  that  the  earth  is  spherical  are  more  in- 
teresting. After  discussing  and  rejecting  various  other 
suggested  forms,  he  points  out  that  an  eclipse  of  the  moon 
is  caused  by  the  shadow  of  the  earth  cast  by  the  sun,  and 

*  I  have  introduced  here  the  familiar  explanation  of  the  phases  of 
the  moon,  and  the  argument  based  on  it  for  the  spherical  shape  of 
the  moon,  because,  although  probably  known  before  Aristotle,  there 
is,  as  far  as  I  know,  no  clear  and  definite  statement  of  the  matter  in 
any  earlier  writer,  and  after  his  time  it  becomes  an  accepted  part  of 
Greek  elementary  astronomy.  It  may  be  noticed  that  the  explanation 
is  unaffected  either  by  the  question  of  the  rotation  of  the  earth  or 
by  that  of  its  motion  round  the  sun. 


32  A  Short  History  of  Astronomy  [CH.  n. 

argues  from  the  circular  form  of  the  boundary  of  the  shadow 
as  seen  on  the  face  of  the  moon  during  the  progress  of  the 
eclipse,  or  in  a  partial  eclipse,  that  the  earth  must  be 
spherical ;  for  otherwise  it  would  cast  a  shadow  of  a  dif- 
ferent shape.  A  second  reason  for  the  spherical  form  of 
the  earth  is  that  when  we  move  north  and  south  the  stars 
change  their  positions  with  respect  to  the  horizon,  while 
some  even  disappear  and  fresh  ones  take  their  place.  This 
shows  that  the  direction  of  the  stars  has  changed  as  com- 
pared with  the  observer's  horizon;  hence,  the  actual  direction 
of  the  stars  being  imperceptibly  affected  by  any  motion  of 
the  observer  on  the  earth,  the  horizons  at  two  places,  north 
and  south  of  one  another,  are  in  different  directions,  and  the 

earth  is  therefore  curved.     For 

,g       example,  if  a  star  is  visible  to  an 
observer  at  A  (fig.  12),  while  to 
an  observer  at  B  it  is  at  the  same 
time  invisible,  i.e.  hidden  by  the 
earth,  the   surface  of  the  earth 
FIG.  i2.— The  curvature  of      at  A  must  be  in  a  different  direc- 
the  earth.  tion  from  that  at  B.      Aristotle 

quotes  further,  in  confirmation  of 

the  roundness  of  the  earth,  that  travellers  from  the  far 
East  and  the  far  West  (practically  India  and  Morocco) 
alike  reported  the  presence  of  elephants,  whence  it  may  be 
inferred  that  the  two  regions  in  question  are  not  very  far 
apart.  He  also  makes  use  of  some  rather  obscure  arguments 
of  an  a  priori  character. 

There  can  be  but  little  doubt  that  the  readiness  with 
which  Aristotle,  as  well  as  other  Greeks,  admitted  the 
spherical  form  of  the  earth  and  of  the  heavenly  bodies, 
was  due  to  the  affection  which  the  Greeks  always  seem 
to  have  had  for  the  circle  and  sphere  as  being  "  perfect," 
i.e.  perfectly  symmetrical'  figures. 

30.  Aristotle  argues  against  the  possibility  of  the  revo- 
lution of  the  earth  round  the  sun,  on  the  ground  that  this 
motion,  if  it  existed,  ought  to  produce  a  corresponding 
apparent  motion  of  the  stars.  We  have  here  the  first 
appearance  of  one  of  the  most  serious  of  the  many  objections 
ever  brought  against  the  belief  in  the  motion  of  the  earth, 
an  objection  really  only  finally  disposed  of  during  the 


$  3oJ  Aristotle  33 

present  century  by  the  discovery  that  such  a  motion  of 
the  stars  can  be  seen  in  a  few  cases,  though  owing  to  the 
almost  inconceivably  great  distance  of  the  stars  the  motion 
is  imperceptible  except  by  extremely  refined  methods  of 
observation  (cf.  chapter  xin.,  §§  278,  279).  The  question 
of  the  distances  of  the  several  celestial  bodies  is  also 
discussed,  and  Aristotle  arrives  at  the  conclusion  that  the 
planets  are  farther  off  than  the  sun  and  moon,  supporting 
his  view  by  his  observation  of  an  occultation  of  Mars  by 
the  moon  (i.e.  a  passage  of  the  moon  in  front  of  Mars),  and 
by  the  fact  that  similar  observations  had  been  made  in  the 
case  of  other  planets  by  Egyptians  and  Babylonians.  It 
is,  however,  difficult  to  see  why  he  placed  the  planets 
beyond  the  sun,  as  he  must  have  known  that  the  intense 
brilliancy  of  the  sun  renders  planets  invisible  in  its  neigh- 
bourhood, and  that  no  occultations  of  planets  by  the  sun 
could  really  have  been  seen  even  if  they  had  been  reported 
to  have  taken  place.  He  quotes  also,  as  an  opinion  of 
"  the  mathematicians,"  that  the  stars  must  be  at  least  nine 
times  as  far  off  as  the  sun. 

There  are  also  in  Aristotle's  writings  a  number  of  astro- 
nomical speculations,  founded  on  no  solid  evidence  and  of 
little  value ;  thus  among  other  questions  he  discusses  the 
nature  of  comets,  of  the  Milky  Way,  and  of  the  stars,  why 
the  stars  twinkle,  and  the  causes  which  produce  the  various 
celestial  motions. 

In  astronomy,  as  in  other  subjects,  Aristotle  appears 
to  have  collected  and  systematised  the  best  knowledge  of 
the  time ;  but  his  original  contributions  are  not  only  not 
comparable  with  his  contributions  to  the  mental  and  moral 
sciences,  but  are  inferior  in  value  to  his  work  in  other 
natural  sciences,  e.g.  Natural  History.  Unfortunately  the 
Greek  astronomy  of  his  time,  still  in  an  undeveloped  state, 
was  as  it  were  crystallised  in  his  writings,  and  his  great 
authority  was  invoked,  centuries  afterwards,  by  comparatively 
unintelligent  or  ignorant  disciples  in  support  of  doctrines 
which  were  plausible  enough  in  his  time,  but  which  subse- 
quent research  was  shewing  to  be  untenable.  The  advice 
which  he  gives  to  his  readers  at  the  beginning  of  his  ex- 
position of  the  planetary  motions,  to  compare  his  views 
with  those  which  they  arrived  at  themselves  or  met  with 

3 


34  A  Short  History  of  Astronomy  [Cn.  n. 

elsewhere,  might  with  advantage  have  been  noted  and 
followed  by  many  of  the  so-called  Aristotelians  of  the 
Middle  Ages  and  of  the  Renaissance.* 

31.  After   the   time   of  Aristotle   the    centre   of  Greek 
scientific   thought    moved    to    Alexandria.      Founded    by 
Alexander   the   Great   (who   was   for    a   time   a   pupil   of 
Aristotle)  in  332  B.C.,  Alexandria  was  the  capital  of  Egypt 
during  the   reigns   of  the   successive    Ptolemies.      These 
kings,    especially    the   second   of   them,   surnamed   Phila- 
delphos,    were   patrons    of    learning ;   they    founded    the 
famous   Museum,   which  contained   a  magnificent   library 
as  well  as  an  observatory,  and  Alexandria  soon  became 
the  home  of  a  distinguished  body  of  mathematicians  and 
astronomers.      During    the   next   five   centuries   the    only 
astronomers  of  importance,   with  the   great   exception   of 
Hipparchus  (§  37),  were  Alexandrines. 

32.  Among   the    earlier   members    of   the   Alexandrine 
school  were  Aristarchus  of  Samos,  Aristyllus,  and  Timo- 
charis,  three  nearly   contemporary  astronomers  belonging 


FIG.  13. — The  method  of  Aristarchus  for  comparing  the  distances 
of  the  sun  and  moon. 

to  the  first  half  of  the  3rd  century  B.C.  The  views  of 
Aristarchus  on  the  motion  of  the  earth  have  already  been 
mentioned  (§  24).  A  treatise  of  his  On  the  Magnitudes 
and  Distances  of  the  Sun  and  Moon  is  still  extant :  he  there 
gives  an  extremely  ingenious  method  for  ascertaining  the 
comparative  distances  of  the  sun  and  moon.  If,  in  the 
figure,  E,  s,  and  M  denote  respectively  the  centres  of  the 
earth,  sun,  and  moon,  the  moon  evidently  appears  to  an 
observer  at  E  half  full  when  the  angle  E  M  s  is  a  right 
angle.  If  when  this  is  the  case  the  angular  distance 
between  the  centres  of  the  sun  and  moon,  /./.  the  angle 
M  E  s,  is  measured,  two  angles  of  the  triangle  M  E  s  are 

*  See,    for    example,    the   account    of  Galilei's  controversies,   in 
chapter  vi. 


$$  3i,  32]  Aristarchus  35 

known ;  its  shape  is  therefore  completely  determined,  and 
the  ratio  of  its  sides  EM,  E  s  can  be  calculated  without 
much  difficulty.  In  fact,  it  being  known  (by  a  well-known 
result  in  elementary  geometry)  that  the  angles  at  E  and  s 
are  together  equal  to  a  right  angle,  the  angle  at  s  is 
obtained  by  subtracting  the  angle  s  E  M  from  a  right  angle. 
Aristarchus  made  the  angle  at  s  about  3°,  and  hence 
calculated  that  the  distance  of  the  sun  was  from  18  to  20 
times  that  of  the  moon,  whereas,  in  fact,  the  sun  is  about  400 
times  as  distant  as  the  moon.  The  enormous  error  is  due 
to  the  difficulty  of  determining  with  sufficient  accuracy  the 
moment  when  the  moon  is  half  full :  the  boundary  separating 
the  bright  and  dark  parts  of  the  moon's  face  is  in  reality 
(owing  to  the  irregularities  on  the  surface  of  the  moon)  an  ill- 
defined  and  broken  line  (cf.  fig.  53  and  the  frontispiece),  so  that 
the  observation  on  which  Aristarchus  based  his  work  could 
not  have  been  made  with  any  accuracy  even  with  our  modern 
instruments,  much  less  with  those  available  in  his  time. 
Aristarchus  further  estimated  the  apparent  sizes  of  .the  sun 
and  moon  to  be  about  equal  (as  is  shewn,  for  example,  at 
an  eclipse  of  the  sun,  when  the  moon  sometimes  rather  more 
than  hides  the  surface  of  the  sun  and  sometimes  does  not 
quite  cover  it),  and  inferred  correctly  that  the  real  diameters 
of  the  sun  and  moon  were  in  proportion  to  their  distances. 
By  a  method  based  on  eclipse  observations  which  was 
afterwards  developed  by  Hipparchus  (§41),  he  also  found 
that  the  diameter  of  the  moon  was  about  -3-  that  of  the 
earth,  a  result  very  near  to  the  truth ;  and  the  same 
method  supplied  data  from  which  the  distance  of  the  moon 
could  at  once  have  been  expressed  in  terms  of  the  radius 
of  the  earth,  but  his  work  was  spoilt  at  this  point  by  a 
grossly  inaccurate  estimate  of  the  apparent  size  of  the  moon 
(2°  instead  of  £°),  and  his  conclusions  seem  to  contradict 
one  another.  He  appears  also  to  have  believed  the  dis- 
tance of  the  fixed  stars  to  be  immeasurably  great  as 
compared  with  that  of  the  sun.  Both  his  speculative 
opinions  and  his  actual  results  mark  therefore  a  decided 
advance  in  astronomy. 

Timocharis  and  Aristyllus  were  the  first  to  ascertain  and 
to  record  the  positions  of  the  chief  stars,  by  means  of 
numerical  measurements  of  their  distances  from  fixed 


A  Short  History  of  Astronomy 


[CH.  IL 


positions  on  the  sky ;  they  may  thus  be  regarded  as  the 
authors  of  the  first  real  star  catalogue,  earlier  astronomers 
having  only  attempted  to  fix  the  position  of  the  stars  by 
more  or  less  vague  verbal  descriptions.  They  also  made  a 
number  of  valuable  observations  of  the  planets,  the  sun, 
etc.,  of  which  succeeding  astronomers,  notably  Hipparchus 
and  Ptolemy,  were  able  to  make  good  use. 

33.  Among  the  important  contributions  of  the  Greeks 
to  astronomy  must  be  placed  the  development,  chiefly  from 
the  mathematical  point  of  view,  of  the  consequences  of  the 
rotation  of  the  celestial  sphere  and  of  some  of  the  simpler 
motions  of  the  celestial  bodies,  a  development  the  indi- 
vidual steps  of  which  it  is  difficult  to  trace.  We  have, 


FIG.  14. — The  equator  and  the  ecliptic. 

however,  a  series  of  minor  treatises  or  textbooks,  written 
for  the  most  part  during  the  Alexandrine  period,  dealing 
with  this  branch  of  the  subject  (known  generally  as 
Spherics,  or  the  Doctrine  of  the  Sphere),  of  which  the 
Phenomena  of  the  famous  geometer  Euclid  (about  300  B.C.) 
is  a  good  example.  In  addition  to  the  points  and  circles 
of  the  sphere  already  mentioned  (chapter  i.,  §§  8-n),  we 
now  find  explicitly  recognised  the  horizon,  or  the  great 
circle  in  which  a  horizontal  plane  thrdugh  the  observer 
meets  the  celestial  sphere,  and  its  pole,*  the  zenith,f  or 

*  The  poles  of  a  great  circle  on  a  sphere  are  the  ends  of  a  diameter 
perpendicular  to  the  plane  of  the  great  circle.  Every  point  on  the 
great  circle  is  at  the  same  distance,  90°,  from  each  pole. 

f  The  word  "zenith  "  is  Arabic,  not  Creek  :  cf.  chapter  in.,  §  64. 


to  33-35]  Spherics  37 

point  on  the  celestial  sphere  vertically  above  the  observer ; 
the  verticals,  or  great  circles  through  the  zenith,  meeting  the 
horizon  at  right  angles ;  and  the  declination  circles,  which 
pass  through  the  north  and  south  poles  and  cut  the 
equator  at  right  angles.  Another  important  great  circle 
was  the  meridian,  passing  through  the  zenith  and  the  poles. 
The  well-known  Milky  Way  had  been  noticed,  and  was 
regarded  as  forming  another  great  circle.  There  are  also 
traces  of  the  two  chief  methods  in  common  use  at  the 
present  day  of  indicating  the  position  of  a  star  on  the 
celestial  sphere,  namely,  by  reference  either  to  the  equator 
or  to  the  ecliptic.  If  through  a  star  s  we  draw  on  the 
sphere  a  portion  of  a  great  circle  s  N,  cutting  the  ecliptic  r  N 
at  right  angles  in  N,  and  another  great  circle  (a  declination 
circle)  cutting  the  equator  at  M,  and  if  r  be  the  first  point  of 
Aries  (§  13),  where  the  ecliptic  crosses  the  equator,  then 
the  position  of  the  star  is  completely  defined  either  by  the 
lengths  of  the  arcs  r  N,  N  s,  which  are  called  the  celestial 
longitude  and  latitude  respectively,  or  by  the  arcs  r  M,  M  s, 
called  respectively  the  right  ascension  and  declination.* 
For  some  purposes  it  is  more  convenient  to  find  the 
position  of  the  star  by  the  first  method,  i.e.  by  reference 
to  the  ecliptic ;  for  other  purposes  in  the  second  way,  by 
making  use  of  the  equator. 

34.  One  of  the  applications  of  Spherics  was  to  the  con- 
struction of  sun-dials,  which  were  supposed  to  have  been 
originally  introduced  into  Greece  from  Babylon,  but  which 
were  much  improved  by  the  Greeks,  and  extensively  used 
both  in  Greek  and  in  mediaeval  times.    The  proper  gradua- 
tion  of  sun-dials   placed   in  various  positions,  horizontal, 
vertical,  and  oblique,  required  considerable  mathematical 
skill.     Much  attention  was  also  given  to  the  time  of  the 
rising  and   setting   of  the   various   constellations,  and   to 
similar  questions. 

35.  The  discovery   of  the  spherical  form  of  the   earth 
led  to  a  scientific  treatment  of  the  differences  between  the 
seasons  in  different  parts  of  the  earth,  and  to  a  correspond- 
ing division  of  the  earth   into   zones.     We  have   already 
seen  that  the  height  of  the  pole  above  the  horizon  varies  in 

*  Most  of  these  names  are  not  Greek,  but  of  later  origin. 


A  Short  History  of  Astronomy 


[CH.    II. 


different  places,  and  that  it  was  recognised  that,  if  a  traveller 
were  to  go  far  enough  north,  he  would  find  the  pole  to 
coincide  with  the  zenith,  whereas  by  going  south  he  would 
reach  a  region  (not  very  far  beyond  the  limits  of  actual 
Greek  travel)  where  the  pole  would  be  on  the  horizon 
and  the  equator  consequently  pass  through  the  zenith  ;  in 
regions  still  farther  south  the  north  pole  would  be  per- 
manently invisible,  and  the  south  pole  would  appear  above 
the  horizon. 

Further,  if  in  the  figure  H  E  K  w  represents  the  horizon, 
meeting  the  equator  Q  E  R  w  in  the  east  and  west  points  E  w, 
and  the  meridian  H  Q  z  P  K  in  the  south  and  north  points 

H  and  K,  z  being  the  zenith 
and  P  the  pole,  then  it  is 
easily  seen  that  Q  z  is  equal 
to  P  K,  the  height  of  the 
pole  above  the  horizon. 
Any  celestial  body,  there- 
fore, the  distance  of  which 
from  the  equator  towards 
the  north  (declination)  is 
less  than  P  K,  will  cross 
the  meridian  to  the  south 
of  the  zenith,  whereas  if 
its  declination  be  greater 
than  P  K,  it  will  cross  to 
the  north  of  the  zenith. 
Now  the  greatest  distance 
of  the  sun  from  the  equator  is  equal  to  the  angle  between 
the  ecliptic  and  the  equator,  or  about  23^°.  Consequently 
at  places  at  which  the  height  of  the  pole  is  less  than  23!° 
the  sun  will,  during  part  of  the  year,  cast  shadows  at  midday 
towards  the  south.  This  was  known  actually  to  be  the  case 
not  very  far  south  of  Alexandria.  It  was  similarly  recog- 
nised that  on  the  other  side  of  the  equator  there  must  be 
a  region  in  which  the  sun  ordinarily  cast  shadows  towards 
the  south,  but  occasionally  towards  the  north.  These  two 
regions  are  the  torrid  zones  of  modem  geographers. 

Again,  if  the  distance  of  the  sun  from  the  equator 
is  23^°,  its  distance  from  the  pole  is  66|°;  therefore  in 
regions  so  far  north  that  the  height  P  K  of  the  north  pole 


FIG.  15. — The  equator,  the  horizon, 
and  the  meridian. 


§  36]          .        The  Measurement  of  the  Earth  39 

is  more  than  66|c,  the  sun  passes  in  summer  into  the 
region  of  the  circumpolar  stars  which  never  set  (chapter  i., 
§  9),  and  therefore  during  a  portion  of  the  summer  the  sun 
remains  continuously  above  the  horizon.  Similarly  in  the 
same  regions  the  sun  is  in  winter  so  near  the  south  pole 
that  for  a  time  it  remains  continuously  below  the  horizon. 
Regions  in  which  this  occurs  (our  Arctic  regions)  were 
unknown  to  Greek  travellers,  but  their  existence  was  clearly 
indicated  by  the  astronomers. 

36.  To  Eratosthenes  (276  B.C.  to  195  or  196  B.C.),  another 
member  of  the  Alexandrine  school,  we  owe  one  of  the  first 
scientific  estimates  of  the  size  of  the  earth.  He  found 


FIG.  1 6. — The  measurement  of  the  earth. 

that  at  the  summer  solstice  the  angular  distance  of  the 
sun  from  the  zenith  at  Alexandria  was  at  midday  -^h  °f 
a  complete  circumference,  or  about  7°,  whereas  at  Syene 
in  Upper  Egypt  the  sun  was  known  to  be  vertical  at 
the  same  time.  From  this  he  inferred,  assuming  Syene 
to  be  due  south  of  Alexandria,  that  the  distance  from 
Syene  to  Alexandria  was  also  yVn  of  the  circumference 
of  the  earth.  Thus  if  in  the  figure  s  denotes  the  sun,  A 
and  B  Alexandria  and  Syene  respectively,  c  the  centre  of 
the  earth,  and  A  z  the  direction  of  the  zenith  at  Alexandria, 
Eratosthenes  estimated  the  angle  s  A  z,  which,  bwing  to 
the  great  distance  of  s,  is  sensibly  equal  to  the  angle  s  c  A, 
to  be  7°,  and  hence  inferred  that  the  arc  A  B  was  to  the 
circumference  of  the  earth  in  the  proportion  of  7°  to  360° 
or  i  to  50.  The  distance  between  Alexandria  and  Syene 


40  A  Short  History  of  Astronomy  [Cn.  II 

being  known  to  be  5,000  stadia,  Eratosthenes  thus  arrived 
at  250,000  stadia  as  an  estimate  of  the  circumference 
of  the  earth,  a  number  altered  into  252,000  in  order  to 
give  an  exact  number  of  stadia  (700)  for  each  degree  on  the 
earth.  It  is  evident  that  the  data  employed  were  rough, 
though  the  principle  of  the  method  is  perfectly  sound ; 
it  is,  however,  difficult  to  estimate  the  correctness  of  the 
result  on  account  of  the  uncertainty  as  to  the  value  of 
the  stadium  used.  If,  as  seems  probable,  it  was  the 
common  Olympic  stadium,  the  result  is  about  20  per  cent. 
too  great,  but  according  to  another  interpretation  *  the 
result  is  less  than  i  per  cent,  in  error  (cf.  chapter  x.,  §  221). 

Another  measurement  due  to  Eratosthenes  was  that 
of  the  obliquity  of  the  ecliptic,  which  he  estimated  at 
f§  of  a  right  angle,  or  23°  51',  the  error  in  which  is  only 
about -7'. 

37.  An  immense  advance  in  astronomy  was  made  by 
HipparchuS)  whom  all  competent  critics  have  agreed  to 
rank  far  above  any  other  astronomer  of  the  ancient  world, 
and  who  must  stand  side  by  side  with  the  greatest  astro- 
nomers of  all  time.  Unfortunately  only  one  unimportant 
book  of  his  has  been  preserved,  and  our  knowledge  of 
his  work  is  derived  almost  entirely  from  the  writings  of  his 
great  admirer  and  disciple  Ptolemy,  who  lived  nearly  three 
centuries  later  (§§  46  seqq.).  We  have  also  scarcely  any 
information  about  his  life.  He  was  born  either  at  Nicaea 
in  Bithynia  or  in  Rhodes,  inf  which  island  he  erected  an 
observatory  and  did  most  of  his  work.  There  is  no 
evidence  that  he  belonged  to  the  Alexandrine  school, 
though  he  probably  visited  Alexandria  and  may  have  made 
some  observations  there.  Ptolemy  mentions  observations 
made  by  him  in  146  B.C.,  126  B.C.,  and  at  many  inter- 
mediate dates,  as  well  as  a  rather  doubtful  one  of  161  B.C. 
The  period  of  his  greatest  activity  must  therefore  have  been 
about  the  middle  of  the  2nd  century  B.C. 

Apart  from  individual  astronomical  discoveries,  his  chief 
services  to  astronomy  may  be  put  under  four  heads.  He 
invented  or  greatly  developed  a  special  branch  of  mathe- 

*  That  of  M.  Paul  Tannery :  Recherches  sur  VHistoire  de  V  Astro- 
nomie  Ancienne,  chap.  v. 


tt  37,  38]  Hipparchus  41 

matics,*  which  enabled  processes  of  numerical  calculation 
to  be  applied  to  geometrical  figures,  whether  in  a  plane  or 
on  a  sphere.  He  made  an  extensive  series  of  observations, 
taken  with  all  the  accuracy  that  his  instruments  would 
permit.  He  systematically  and  critically  made  use  of  old 
observations  for  comparison  with  later  ones  so  as  to 
discover  astronomical  changes  too  slow  to  be  detected 
within  a  single  lifetime.  Finally,  he  systematically  employed 
a  particular  geometrical  scheme  (that  of  eccentrics,  and  to 
a  less  extent  that  of  epicycles)  for  the  representation  of  the 
motions  of  the  sun  and  moon. 

38.  The  merit  of  suggesting  that  the  motions  of  the 
heavenly  bodies  could  be  represented  more  simply  by  com- 
binations of  uniform  circular  motions  than  by  the  revolv- 
ing spheres  of  Eudoxus  and  his  school  (§  26)  is  generally 
attributed  to  the  great  Alexandrine  mathematician  Apol- 
lonius  of  Perga,  who  lived  in  the  latter  half  of  the  3rd 
century  B.C.,  but  there  is  no  clear  evidence  that  he  worked 
out  a  system  in  any  detail. 

On  account  of  the  important  part  that  this  idea  played 
in  astronomy  for  nearly  2,000  years,  it  may  be  worth 
while  to  examine  in  some  detail  Hipparchus's  theory  of 
the  sun,  the  simplest  and  most  successful  application  of 
the  idea. 

We  have  already  seen  (chapter  i.,  §  10)  that,  in  addition 
to  the  daily  motion  (from  east  to  west)  which  it  shares  with 
the  rest  of  the  celestial  bodies,  and  of  which  we  need  here 
take  no  further  account,  the  sun  has  also  an  annual  motion 
on  the  celestial  sphere  in  the  reverse  direction  (from  west 
to  east)  in  a  path  oblique  to  the  equator,  which  was  early 
recognised  as  a  great  circle,  called  the  ecliptic.  It  must 
be  remembered  further  that  the  celestial  sphere,  on  which 
the  sun  appears  to  lie,  is  a  mere  geometrical  fiction 
introduced  for  convenience ;  all  that  direct  observation 
gives  is  the  change  in  the  sun's  direction,  and  therefore 
the  sun  may  consistently  be  supposed  to  move  in  such  a 
way  as  to  vary  its  distance  from  the  earth  in  any  arbitrary 
manner,  provided  only  that  the  alterations  in  the  apparent 
size  of  the  sun,  caused  by  the  variations  in  its  distance, 
agree  with  those  observed,  or  that  at  any  rate  the  differences 
*  Trigonometry. 


42  A  Short  History  of  Astronomy  [Cn.  II. 

are  not  great  enough  to  be  perceptible.  It  was,  moreover, 
known  (probably  long  before  the  time  of  Hipparchus)  that 
the  sun's  apparent  motion  in  the  ecliptic  is  not  quite 
uniform,  the  motion  at  some  times  of  the  year  being 
slightly  more  rapid  than  at  others. 

Supposing  that  we  had  such  a  complete  set  of  observa- 
tions of  the  motion  of  the  sun,  that  we  knew  its  position 
from  day  to  day,  how  should  we  set  to  work  to  record  and 
describe  its  motion  ?  For  practical  purposes  nothing  could 
be  more  satisfactory  than  the  method  adopted  in  our 
almanacks,  of  giving  from  day  to  day  the  position  of  the 
sun  ;  after  observations  extending  over  a  few  years  it  would 
not  be  difficult  to  verify  that  the  motion  of  the  sun  is  (after 
allowing  for  the  irregularities  of  our  calendar)  from  year  to 
year  the  same,  and  to  predict  in  this  way  the  place  of  the 
sun  from  day  to  day  in  future  years. 

But  it  is  clear  that  such  a  description  would  not  only 
be  long,  but  would  be  felt  as  unsatisfactory  by  any  one 
who  approached  the  question  from  the  point  of  view  of 
intellectual  curiosity  or  scientific  interest.  Such  a  person 
would  feel  that  these  detailed  facts  ought  to  be  capable 
of  being  exhibited  as  consequences  of  some  simpler  general 
statement. 

A  modern  astronomer  would  effect  this  by  expressing 
the  motion  of  the  sun  by  means  of  an  algebraical  formula, 
i.e.  he  would  represent  the  velocity  of  the  sun  or  its 
distance  from  some  fixed  point  in  its  path  by  some 
symbolic  expression  representing  a  quantity  undergoing 
changes  with  the  time  in  a  certain  definite  way,  and 
enabling  an  expert  to  compute  with  ease  the  required 
position  of  the  sun  at  any  assigned  instant.* 

The  Greeks,  however,  had  not  the  requisite  algebraical 
knowledge  for  such  a  method  of  representation,  and  Hip- 
parchus, like  his  predecessors,  made  use  of  a  geometrical 

*  The  process  may  be  worth  illustrating  by  means  of  a  simpler 
problem.  A  heavy  bod}*,  falling  freely  under  gravity,  is  found  (the 
resistance  of  the  air  being  allowed  for)  to  fall  about  16  feet  in 
I  second,  64  feet  in  2  seconds,  144  feet  in  3  seconds,  256  feet  in 
4  seconds,  400  feet  in  5  seconds,  and  so  on.  This  series  of  figures 
carried  on  as  far  as  may  be  required  would  satisfy  practical  re- 
quirements, supplemented  if  desired  by  the  corresponding  figures 
for  fractions  of  seconds;  but  the  mathematician  represents  the  same 


$  39J  Hipparchus  43 

representation  of  the  required  variations  in  the  sun's  motion 
in  the  ecliptic,  a  method  of  representation  which  is  in  some 
respects  more  intelligible  and  vivid  than  the  use  of  algebra, 
but  which  becomes  unmanageable  in  complicated  cases. 
It  runs  moreover  the  risk  of  being  taken  for  a  mechanism. 
The  circle,  being  the  simplest  curve  known,  would  naturally 
be  thought  of,  and  as  any  motion  other  than  a  uniform 
motion  would  itself  require  a  special  representation,  the 
idea  of  Apollonius,  adopted  by  Hipparchus,  was  to  devise 
a  proper  combination  of  uniform  circular  motions. 

39.  The  simplest  device  that  was  found  to  be  satisfactory 
in  the  case  of  the  sun  was  the  use  of  the  eccentric,  i.e.  a 
circle  the  centre  of  which  (c)  does  not  coincide  with  the 
position  of  the  observer  on  the  earth  (E).  If  in  fig.  17  a 
point,  s,  describes  the  eccentric  circle  A  F  G  B  uniformly, 
so  that  it  always  passes  over  equal  arcs  of  the  circle  in 
equal  times  and  the  angle  ACS  increases  uniformly,  then 
it  is  evident  that  the  angle  A  E  s,  or  the  apparent  distance 
of  s  from  A,  does  not  increase  uniformly.  When  s  is  near 
the  point  A,  which  is  farthest  from  the  earth  and  hence 
called  the  apogee,  it  appears  on  account  of  its  greater 
distance  from  the  observer  to  move  more  slowly  than  when 
near  F  or  G  ;  and  it  appears  to  move  fastest  when  near  B, 
the  point  nearest  to  E,  hence  called  the  perigee.  Thus  the 
motion  of  s  varies  in  the  same  sort  of  way  as  the  motion 
of  the  sun  as  actually  observed.  Before,  however,  the 
eccentric  could  be  considered  as  satisfactory,  it  was  neces- 
sary to  show  that  it  was  possible  to  choose  the  direction 
of  the  line  B  E  c  A  (the  line  of  apses)  which  determines  the 
positions  of  the  sun  when  moving  fastest  and  when  moving 
most  slowly,  and  the  magnitude  of  the  ratio  of  E  c  to  the 
radius  c  A  of  the  circle  (the  eccentricity),  so  as  to  make 
the  calculated  positions  of  the  sun  in  various  parts  of  its 
path  differ  from  the  observed  positions  at  the  corresponding 

facts  more  simply  and  in  a  way  more  satisfactory  to  the  mind  by  the 
formula  5  =  16  f',  where  s  denotes  the  number  of  feet  fallen,  and 
t  the  number  of  seconds.  By  giving  t  any  assigned  value,  the 
corresponding  space  fallen  through  is  at  once  obtained.  Similarly 
the  motion  of  the  sun  can  be  represented  approximately  by  the 
more  complicated  formula  /  =  nt  +  2  e  sin  nt,  where  /  is  the 
distance  from  a  fixed  point  in  the  orbit,  t  the  time,  and  n,  e  certain 
numerical  quantities. 


44 


A  Short  History  of  Astronomy 


[CH.    II. 


times  of  year  by  quantities  so  small  that  they  might  fairly 
be  attributed  to  errors  of  observation. 

This  problem  was  much  more  difficult  than  might  at  first 
sight  appear,  on  account  of  the  great  difficulty  experienced 
in  Greek  times  and  long  afterwards  in  getting  satisfactory 
observations  of  the  sun.  As  the  sun  and  stars  are  not 
visible  at  the  same  time,  it  is  not  possible  to  measure 
directly  the  distance  of  the  sun  from  neighbouring  stars 
a,nd  so  to  fix  its  place  on  the  celestial  sphere.  But  it 


FIG.  17. — The  eccentric. 

is  possible,  by  measuring  the  length  of  the  shadow  cast  by 
a  rod  at  midday,  to  ascertain  with  fair  accuracy  the  height 
of  the  sun  above  the  horizon,  and  hence  to  deduce  its 
distance  from  the  equator,  or  the  declination  (figs.  3,  14). 
This  one  quantity  does  not  suffice  to  fix  the  sun's  position, 
but  if  also  the  sun's  right  ascension  (§  33),  or  its  distance 
east  and  west  from  the  stars,  can  be  accurately  ascertained, 
its  place  on  the  celestial  sphere  is  completely  determined. 
The  methods  available  for  determining  this  second  quantity 
were,  however,  very  imperfect.  One  method  was  to  note 
the  time  between  the  passage  of  the  sun  across  some  fixed 
position  in  the  sky  (e.g.  the  meridian),  and  the  passage  o'f 


$  39]  Hipparchus  45 

a  star  across  the  same  place,  and  thus  to  ascertain  the 
angular  distance  between  them  (the  celestial  sphere  being 
known  to  turn  through  15°  in  an  hour),  a  method  which 
with  modern  clocks  is  extremely  accurate,  but  with  the 
rough  water-clocks  or  sand-glasses  of  former  times  was  very 
uncertain.  In  another  method  the  moon  was  used  as  a 
connecting  link  between  sun  and  stars,  her  position  relative 


P 
FIG.  1 8. — The  position  of  the  sun's  apogee. 

to  the  latter  being  observed  by  night,  and  with  respect  to 
the  former  by  day ;  but  owing  to  the  rapid  motion  of  the 
moon  in  the  interval  between  the  two  observations,  this 
method  also  was  not  susceptible  of  much  accuracy. 

In  the  case  of  the  particular  problem  of  the  deter- 
mination of  the  line  of  apses,  Hipparchus  made  use  of 
another  method,  and  his  skill  is  shewn  in  a  striking  manner 
by  his  recognition  that  both  the  eccentricity  and  position 
of  the  apse  line  could  be  determined  from  a  knowledge  of 


46  A  Short  History  of  Astronomy  [CH.  n. 

the  lengths  of  two  of  the  seasons  of  the  year,  i.e.  of  the 
intervals  'into  which  the  year  is  divided  by  the  solstices 
and  the  equinoxes  (§  n).  By  means  of  his  own  observa- 
tions, and  of  others  made  by  his  predecessors,  he  ascer-. 
tained  the  length  of  the  spring  (from  the  vernal  equinox  to 
the  summer  solstice)  to  be  94  days,  and  that  of  the  summer 
(summer  solstice  to  autumnal  equinox)  to  be  92^  days,  the 
length  of  the  year  being  365 \  days.  As  the  sun  moves 
in  each  season  through  the  same  angular  distance,  a  right 
angle,  and  as  the  spring  and  summer  make  together  more 
than  half  the  year,  and  the  spring  is  longer  than  the 
summer,  it  follows  that  the  sun  must,  on  the  whole,  be 
moving  more  slowly  during  the  spring  than  in  any  other 
season,  and  that  it  must  therefore  pass  through  the  apogee 
in  the  spring.  If,  therefore,,  in  fig.  18,  we  draw  two 
perpendicular  lines  Q  E  s,  p  E  R  to  represent  the  directions 
of  the  sun  at  the  solstices  and  equinoxes,  p  corresponding 
to  the  vernal  equinox  and  R  to  the  autumnal  equinox,  the 
apogee  must  lie  at  some  point  A  between  p  and  Q.  So 
much  can  be  seen  without  any  mathematics :  the  actual 
calculation  of  the  position  of  A  and  of  the  eccentricity  is 
a  matter  of  some  complexity.  The  angle  PEA  was  found 
to  be  about  65°,  so  that  the  sun  would  pass  through  its 
apogee  about  the  beginning  of  June  ;  and  the  eccentricity 
was  estimated  at  ^V 

The  motion  being  thus  represented  geometrically,,  it 
became  merely  a  matter  of  not  very  difficult  calculation  to 
construct  a  table  from  which  the  position  of  the  sun  for 
any  day  in  the  year  could  be  easily  deduced.  This  was 
done  by  computing  the  so-called  equation  of  the  centre, 
the  angle  c  s  E  of  fig.  17,  which  is  the  excess  of  the  actual 
longitude  of  the  sun  over  the  longitude  which  it  would 
have  had  if  moving  uniformly. 

Owing  to  the  imperfection  of  the  observations  used 
(Hipparchus  estimated  that  the  times  of  the  equinoxes  and 
solstices  could  only  be  relied  upon  to  within  about  half  a 
day),  the  actual  results  obtained  were  not,  according  to 
modern  ideas,  very  accurate,  but  the  theory  represented 
the  sun's  motion  with  an  accuracy  about  as  great  as  that 
of  the  observations.  It  is  worth  noticing  that  with  the 
same  theory,  but  with  an  improved  value  of  the  eccentricity, 


$  4°]  Hipparchus  47 

the  motion  of  the  sun  can  be  represented  so  accurately 
that  the  error  never  exceeds  about  i',  a  quantity  insensible 
to  the  naked  eye. 

The  theory  of  Hipparchus  represents  the  variations  in 
the  distance  of  the  sun  with  much  less  accuracy,  and 
whereas  in  fact  the  angular  diameter  of  the  sun  varies  by 
about  ^t:h  part  of  itself,  or  by  about  i'  in  the  course  of 
the  year,  this  variation  according  to  Hipparchus  should  be 
about  twice  as  great.  But  this  error  would  also  have  been 
quite  imperceptible  with  his  instruments. 

Hipparchus  saw  that  the  motion  of  the  sun  could  equally 
well  be  represented  by  the  other  device  suggested  by 
Apojlonius,  the  epi- 
cycle. The  body  the 
motion  of  which  is  to  be 
represented  is  supposed 
to  move  uniformly 
round  the  circumference 
of  one  circle,  called  the 
epicycle,  the  centre  of 
which  in  turn  moves  on 
another  circle  called  the 
deferent.  It  is  in  fact 
evident  that  if  a  circle 
equal  to  the  eccentric, 
but  with  its  centre  at  E 
(fig.  19),  be  taken  as  FIG.  19. — The  epicycle  and  the  deferent, 
the  deferent,  and  if  s' 

be  taken  on  this  so  that  E  s'  is  parallel  to  c  s,  then  s'  s  is 
parallel  and  equal  to  E  c ;  and  that  therefore  the  sun  s,  moving 
uniformly  on  the  eccentric,  may  equally  well  be  regarded 
as  lying  on  a  circle  of  radius  s'  s,  the  centre  s'  of  which 
moves  on  the  deferent.  The  two  constructions  lead  in 
fact  in  this  particular  problem  to  exactly  the  same  result, 
and  Hipparchus  chose  the  eccentric  as  being  the  simpler. 

40.  The  motion  of  the  moon  being  much  more  com- 
plicated than  that  of  the  sun  has  always  presented  difficulties 
to  astronomers,*  and  Hipparchus  required  for  it  a  more 
elaborate  construction.  Some  further  description  of  the 

*  At  the  present  time  there  is  still  a  small  discrepancy  between  the 
observed  and  calculated  places  of  the  moon.  See  chapter  xin.,  §  290. 


48  A  Short  History  of  Astronomy  [CH.  n. 

moon's  motion  is,  however,  necessary  before  discussing  his 
theory. 

We  have  already  spoken  (chapter  i.,  §  16)  of  the  lunar 
month  as  the  period  during  which  the  moon  returns  to  the 
same  position  with  respect  to  the  sun ;  more  precisely  this 
period  (about  29!  days)  is  spoken  of  as  a  lunation  or 
synodic  month:  as,  however,  the  sun  moves  eastward  on 
the  celestial  sphere  like  the  moon  but  more  slowly,  the 
moon  returns  to  the  same  position  with  respect  to  the 
stars  in  a  somewhat  shorter  time  ;  this  period  (about  27 
days  8  hours)  is  known  as  the  sidereal  month,  Again,  the 
moon's  path  on  the  celestial  sphere  is  slightly  inclined  to 
the  ecliptic,  and  may  be  regarded  approximately  as  a  great 
circle  cutting  the  ecliptic  in  two  nodes,  at  an  angle  which 
Hipparchus  was  probably  the  first  to  fix  definitely  at 
about  5°.  Moreover,  the  moon's  path  is  always  changing 
in  such  a  way  that,  the  inclination  to  the  ecliptic  remaining 
nearly  constant  (but  cf.  chapter  v.,  §  in),  the  nodes  move 
slowly  backwards  (from  east  to  west)  along  the  ecliptic, 
performing  a  complete  revolution  in  about  19  years.  It  is 
therefore  convenient  to  give  a  special  name,  the  draconitic 
month,*  to  the  period  (about  27  days  5  hours)  during  which 
the  moon  returns  to  the  same  position  with  respect  to  the 
nodes. 

Again,  the  motion  of  the  moon,  like  that  of  the  sun,  is 
not  uniform,  the  variations  being  greater  than  in  the  case 
of  the  sun.  Hipparchus  appears  to  have  been  the  first  to 
discover  that  the  part  of  the  moon's  path  in  which  the 
motion  is  most  rapid  is  not  always  in  the  same  position  on 
the  celestial  sphere,  but  moves  continuously ;  or,  in  other 
words,  that  the  line  of  apses  (§  39)  of  the  moon's  path 
moves.  The  motion  is  an  advance,  and  a  complete  circuit 
is  described  in  about  nine  years.  Hence  arises  a  fourth 
kind  of  month,  the  anomalistic  month,  which  is  the  period 
in  which  the  moon  returns  to  apogee  or  perigee. 

To  Hipparchus  is  due  the  credit  of  fixing  with  greater 

*  The  name  is  interesting  as  a  remnant  of  a  very  early  supersti- 
tion. Eclipses,  which  always  occur  near  the  nodes,  were  at  one 
time  supposed  to  be  caused  by  a  dragon  which  devoured  the  sun 
or  moon.  The  symbols  8  $3  still  used  to  denote  the  two  nodes 
are  supposed  to  represent  the  head  and  tail  of  the  dragon. 


«  4il  Hipparchus  49 

exactitude  than  before  the  lengths  of  each  of  these  months. 
In  order  to  determine  them  with  accuracy  he  recognised 
the  importance  of  comparing  observations  of  the  moon 
taken  at  as  great  a  distance  of  time  as  possible,  and  saw 
that  the  most  satisfactory  results  could  be  obtained  by 
using  Chaldaean  and  other  eclipse  observations,  which, 
as  eclipses  only  take  place  near  the  moon's  nodes,  were 
simultaneous  records  of  the  position  of  the  moon,  the 
nodes,  and  the  sun. 

To  represent  this  complicated  set  of  motions,  Hipparchus 
used,  as  in  the  case  of  the  sun,  an  eccentric,  the  centre  of 
which  described  a  circle  round  the  earth  in  about  nine 
years  (corresponding  to  the  motion  of  the  apses),  the  plane 
of  the  eccentric  being  inclined  to  the  ecliptic  at  an  angle 
of  5°,  and  sliding  back,  so  as  to  represent  the  motion  of 
the  nodes  already  described. 

The  result  cannot,  however,  have  been  as  satisfactory  as 
in  the  case  of  the  sun.  The  variation  in  the  rate  at  which 
the  moon  moves  is  not  only  greater  than  in  the  case  of 
the  sun,  but  follows  a  less  simple  law,  and  cannot  be  ade- 
quately represented  by  means  of  a  single  eccentric ;  so 
that  though  Hipparchus'  work  would  have  represented  the 
motion  of  the  moon  in  certain  parts  of  her  orbit  with  fair 
accuracy,  there  must  necessarily  have  been  elsewhere  dis- 
crepancies between  the  calculated  and  observed  places. 
There  is  some  indication  that  Hipparchus  was  aware  of 
these,  but  was  not  able  to  reconstruct  his  theory  so  as  to 
account  for  them. 

41.  In  the  case  of  the  planets  Hipparchus  found  so 
small  a  supply  of  satisfactory  observations  by  his  prede- 
cessors, that  he  made  no  attempt  to  construct  a  system 
of  epicycles  or  eccentrics  to  represent  their  motion,  but 
collected  fresh  observations  for  the  use  of  his  successors. 
He  also  made  use  of  these  observations  to  determine  with 
more  accuracy  than  before  the  average  times  of  revolution 
of  the  several  planets. 

He  also  made  a  satisfactory  estimate  of  the  size  and 
distance  of  the  moon,  by  an  eclipse  method,  the  leading 
idea  of  which  was  due  to  Aristarchus  (§  32);  by  observing 
the  angular  diameter  of  the  earth's  shadow  (Q  R)  at  the 
distance  of  the  moon  at  the  time  of  an  eclipse,  and  comparing 

4 


5° 


d  Short  History  of  Astronomy 


[CH.   II. 


it  with  the  known  angular  dia- 
meters of  the  sun  and  moon, 
he  obtained,  by  a  simple  cal- 
culation,* a  relation  between 
the  distances  of  the  sun  and 
moon,  which  gives  either  when 

*  In  the  figure,  which  is  taken 
from  the  De  Revolutionibus  of 
Coppernicus  (chapter  iv.,  §  85), 
let  D,  K,  M  represent  respectively 
the  centres  of  the  sun,  earth,  and 
moon,  at  the  time  of  an  eclipse  of 
the  moon,  and  let  s  Q  G,  s  R  E  denote 
the  boundaries  of  the  shadow-cone 
cast  by  the  earth  ;  then  Q  R,  drawn 
at  right  angles  to  the  axis  of  the 
cone,  is  the  breadth  of  the  shadow 
at  the  distance  of  the  moon.  We 
have  then  at  once  from  similar 
triangles 

G  K  — Q  M  :  A  D  — G  K    \\    M  K  :   KD. 

Hence  if  K  D  =  n  .  M  K  and  .-. 
also  AD  =  n  .' (radius 'of  moon),  n 
being  19  according  to  Aristarchus, 
G  K  —  Q  M  :  n  .  (radius  of  moon)  —  G  K 

: :  i :  n 

n  .  (radius  ot  moon)  — GK 

= n G K—H QM 

.'.  radius  of  moon  +  radius  of 
shadow 

=  (i  +~)  (radius  of  earth). 

By  observation  the  angular  radius 
of  the  shadow  was  found  to  be 
about  40'  and  that  of  the  moon  to 
be  15',  so  that 

radius  of  shadow  =  f  radius  of  moon; 
/.  radius  of  moon 

=  IT  (i  +  -)  (radius  of  earth). 
But  the  angular  radius  of  the  moon 
being  15',  its  distance  is  necessarily 
about  220  times  its  radius, 

and  .".  distance  of  the  moon 

=  60  (i  +  -)  (radius  of  the  earth), 

which  is  roughly  Hipparchus's 
result,  if  n  be  any  fairly  large 


FIG.  20.- — The  eclipse  method 
of  connecting  the  distances 
of  the  sun  and  moon. 


*  4z]  Hipparchus  51 

the  other  is  known.  Hipparchus  knew  that  the  sun  was 
very  much  more  distant  than  the  moon,  and  appears  to 
have  tried  more  than  one  distance,  that  of  Aristarchus  among 
them,  and  the  result  obtained  in  each  case  shewed  that 
the  distance  of  the  moon  was  nearly  59  times  the  radius 
of  the  earth.  Combining  the  estimates  of  Hipparchus  and 
Aristarchus,  we  find  the  distance  of  the  sun  to  be  about  1,200 
times  the  radius  of  the  earth — a  number  which  remained  sub- 
stantially unchanged  for  many  centuries  (chapter  VII.L,  §  161 ). 

42.  The  appearance  in  134  B.C.  of  a  new  star  in  the 
Scorpion  is  said  to  have  suggested  to  Hipparchus  the 
construction  of  a  new  catalogue  of  the  stars.  He  included 
i, 080  stars,  and  not  only  gave  the  (celestial)  latitude  and 
longitude  of  each  star,  but  divided  them  according  to  their 
brightness  into  six  magnitudes.  The  constellations  to  which 
he  refers  are  nearly  identical  with  those  of  Eudoxus  (§  26), 
and  the  list  has  undergone  few  alterations  up  to  the  present 
day,  except  for  the  addition  of  a  number  of  southern  con- 
stellations, invisible  in  the  civilised  countries  of  the  ancient 
world.  Hipparchus  recorded  also  a  number  of  cases  in 
which  three  or  more  stars  appeared  to  be  in  line  with  one 
another,  or,  more  exactly,  lay  on  the  same  great  circle, 
his  object  being  to  enable  subsequent  observers  to  detect 
more  easily  possible  changes  in  the  positions  of  the  stars. 
The  catalogue  remained,  with  slight  alterations,  the  standard 
one  for  nearly  sixteen  centuries  (cf.  chapter  in.,  §  63). 

The  construction  of  this  catalogue  led  to  a  notable 
discovery,  the  best  known  probably  of  all  those  which 
Hipparchus  made.  In  comparing  his  observations  of  certain 
stars  with  those  of  Timocharis  and  Aristyllus  (§  33),  made 
about  a  century  and  a  half  earlier,  Hipparchus  found  that 
their  distances  from  the  equinoctial  points  had  changed. 
Thus,  in  the  case  of  the  bright  star  Spica,  the  distance 
from  the  equinoctial  points  (measured  eastwards)  had 
increased  by  about  2°  in  150  years,  or  at  the  rate  of  48"  per 
annum.  Further  inquiry  showed  that,  though  the  roughness 
of  the  observations  produced  considerable  variations  in  the 
case  of  different  stars,  there  was  evidence  of  a  general 
increase  in  the  longitude  of  the  stars  (measured  from  west 
to  east),  unaccompanied  by  any  change  of  latitude,  the 
amount  of  the  change  being  estimated  by  Hipparchus  as 


52  A  Short  History  of  Astronomy  [CH.  n. 

at  least  36"  annually,  and  possibly  more.  The  agreement 
between  the  motions  of  different  stars  was  enough  to 
justify  him  in  concluding  that  the  change  could  be 
accounted  for,  not  as  a  motion  of  individual  stars,  but 
rather  as  a  change  in  the  position  of  the  equinoctial 
points,  from  which  longitudes  were  measured.  Now  these 
points  are  the  intersection  of  the  equator  and  the  ecliptic : 
consequently  one  or  another  of  these  two  circles  must  have 
changed.  But  the  fact  that  the  latitudes  of  the  stars  had 
undergone  no  change  shewed  that  the  ecliptic  must  have 
retained  its  position  and  that  the  change  had  been  caused 


.  FIG.  21. — The  increase  of  the  longitude  of  a  star. 

by  a  motion  of  the  equator.  Again,  Hipparchus  measured 
the  obliquity  of  the  ecliptic  as  several  of  his  predecessors 
had  done,  and  the  results  indicated  no  appreciable  change. 
Hipparchus  accordingly  inferred  that  the  equator  was,  as 
it  were,  slowly  sliding  backwards  (i.e.  from  east  to  west), 
keeping  a  constant  inclination  to  the  ecliptic. 

The  argument  may  be  made  clearer  by  figures.  In 
fig.  21  let  TM  denote  the  ecliptic,  TN  the  equator,  s  a 
star  as  seen  by  Timocharis,  s  M  a  great  circle  drawn  per- 
pendicular to  the  ecliptic.  Then  s  M  is  the  latitude,  TM 
the  longitude.  Let  s'  denote  the  star  as  seen  by  Hipparchus ; 


42] 


Hipparchus 


53 


then  he  found  that  s'  M    was    equal    to   the    former  s  M, 
but  that  TM'  was  greater  than, the  former  TM,  or  that  M' 

S 


M 


FIG.  22. — The  movement  of  the  equator. 


N' 


was   slightly  to  the  east  of  M.     This  change  M  M'  being 

nearly  the  same  for  all  stars,  it  was  simpler  to  attribute  it 

to  an  equal  motion  in   the 

opposite    direction    of   the 

point   r ,  say  from   r  to   r ' 

(fig.  22),  i.e.  by  a  motion  of 

the    equator    from    TN    to 

T'N',  its  inclination  N'  T'M 

remaining  equal  to  its  former 

amount  N  r  M.     The  general 

effect  of  this  change  is  shewn 

in  a  different  way  in  fig.  23, 

where  T  r'  =~  =£='  being  the 

ecliptic,    A  B  c  D   represents 

the  equator  as  it  appeared 

in  the  time  of  Timocharis, 

A'  B'  C'  D'     (printed     in     red)        FIG.  23.— The  precession  of  the 

the    same   in   the    time    of  equinoxes. 

Hipparchus,  r ,  ^  being  the 

earlier  positions  of  the  two  equinoctial  points,  and  r',  =s= 
the  later  positions. 


54 


A  Short  History  of  Astronomy 


[CH.   II. 


The  annual  motion  r  T  '  was,  as  has  been  stated,  estimated 
by  Hipparchus  as  being  at  least  36"  (equivalent  to  one 
degree  in  a  century),  and  probably  more.  Its  true  value  is 
considerably  more,  namely  about  50''. 

An  important  consequence  of  the  motion  of  the  equator 
thus  discovered  is  that  the  sun  in  its  annual  journey  round 
the  ecliptic,  after  starting  from  the  equinoctial  point,  returns 
to  the  new  position  of  the  equinoctial  point  a  little  before 
returning  to  its  original  position  with  respect  to  the  stars, 
and  the  successive  equinoxes  occur  slightly  earlier  than  they 


FIG.  24. — The  precession  of  the  equinoxes. 

otherwise  would.  From  this  fact  is  derived  the  name  pre- 
cession of  the  equinoxes,  or  more  shortly,  precession,  which 
is  applied  to  the  motion  that  we  have  been  considering. 
Hence  it  becomes  necessary  to  recognise,  as  Hipparchus 
did,  two  different  kinds  of  year,  the  tropical  year  or  period 
required  by  the  sun  to  return  to  the  same  position  with 
respect  to  the  equinoctial  points,  and  the  sidereal  year  or 
period  of  return  to  the  same  positioia  with  respect  to  the 
stars.  If  T  r'  denote  the  motion  of  the  equinoctial  point 
during  a  tropical  year,  then  the  sun  after  starting  from  the 


$  42]  Hipparchus  55 

equinoctial  point  at  r  arrives — at  the  end  of  a  tropical 
year — at  the  new  equinoctial  point  at  r ' ;  but  the  sidereal 
year  is  only  complete  when  the  sun  has  further  described 
the  arc  r'r  and  returned  to  its  original  starting-point  T. 
Hence,  taking  the  modem  estimate  50"  of  the  arc  r  r',  the 
sun,  in  the  sidereal  year,  describes  an  arc  of  360°,  in  the 
tropical  year  an  arc  less  by  50",  or  359°  59'  10" ;  the  lengths 
of  the  two  years  are  therefore  in  this  proportion,  and  the 
amount  by  which  the  sidereal  year  exceeds  the  tropical 
year  bears  to  either  the  same  ratio  as  50"  to  360°  (or 

1,296,000"),  and  is  therefore         * — —  days  or  about  20 

1296000 

minutes. 

Another  way  of  expressing  the  amount  of  the  precession 
is  to  say  that  the  equinoctial  point  will  describe  the 
complete  circuit  of  the  ecliptic  and  return  to  the  same 
position  after  about  26,000  years. 

The  length  of  each  kind  of  year  was  also  fixed 
by  Hipparchus  with  considerable  accuracy.  That  of 
the  tropical  year  was  obtained  by  comparing  the  times 
of  solstices  and  equinoxes  observed  by  earlier  astrono- 
mers with  those  observed  by  himself.  He  found,  for 
example,  by  comparison  of  the  date  of  the  summer  solstice 
of  280  B.C.,  observed  by  Aristarchus  of  Samos,  with  that 
of  the  year  135  B.C.,  that  the  current  estimate  of  365 1 
days  for  the  length  of  the  year  had  to  be  diminished 
by  jnj^th  of  a  day  or  about  five  minutes,  an  estimate 
confirmed  roughly  by  other  cases.  It  is  interesting  to 
note  as  an  illustration  of  his  scientific  method  that  he 
discusses  with  some  care  the  possible  error  of  the  observa- 
tions, and  concludes  that  the  time  of  a  solstice  may  be 
erroneous  to  the  extent  of  about  f  day,  while  that  of  an 
equinox  may  be  expected  to  be  within  |  day  of  the  truth. 
In  the  illustration  given,  this  would  indicate  a  possible 
error  of  i|  days  in  a  period  of  145  years,  or  about  15 
minutes  in  a  year.  Actually  his  estimate  of  the  length  of 
the  year  is  about  six  minutes  too  great,  and  the  error  is 
thus  much  less  than  that  which  he  indicated  as  possible. 
In  the  course  of  this  work  he  considered  also  the  possibility 
of  a  change  in  the  length  of  the  year,  and  arrived  at  the 
conclusion  that,  although  his  observations  were  not  precise 


56  A  Short  History  of  Astronomy  [Ca.  n. 

enough  to  show  definitely  the  invariability  of  the  year,  there 
was  no  evidence  to  suppose  that  it  had  changed. 

The  length  of  the  tropical  year  being  thus  evaluated  at 
365  days  5  hours  55  minutes,  and  the  difference  between 
the  two  kinds  of  year  being  given  by  the  observations  of 
precession,  the  sidereal  year  was  ascertained  to  exceed 
365!  days  by  about  TO  minutes,  a  result  agreeing  almost 
exactly  with  modern  estimates.  That  the  addition  of  two 
erroneous  quantities,  the  length  of  the  tropical  year  and  the 
amount  of  the  precession,  gave  such  an  accurate  result  was 
not,  as  at  first  sight  appears,  a  mere  accident.  The  chief 
source  of  error  in  each  case  being  the  erroneous  times  of 
the  several  equinoxes  and  solstices  employed,  the  errors 
in  them  would  tend  to  produce  errors  of  opposite  kinds 
in  the  tropical  year  and  in  precession,  so  that  they  would  in 
part  compensate  one  another.  This  estimate  of  the  length 
of  the  sidereal  year  was  probably  also  to  some  extent 
verified  by  Hipparchus  by  comparing  eclipse  observations 
made  at  different  epochs. 

43.  The  great  improvements  which  Hipparchus  effected 
in  the  theories  of  the  sun  and  moon  naturally  enabled  him 
to  deal  more  successfully  than  any  of  his  predecessors  with 
a  problem  which  in  all  ages  has  been  of  the  greatest  interest, 
the  prediction  of  eclipses  of  the  sun  and  moon. 

That  eclipses  of  the  moon  were  caused  by  the  passage 
of  the  moon  through  the  shadow  of  the  earth  thrown  by 
the  sun,  or,  in  other  words,  by  the  interposition  of  the 
earth  between  the  sun  and  moon,  and  eclipses  of  the  sun 
by  the  passage  of  the  moon  between  the  sun  and  the 
observer,  was  perfectly  well  known  to  Greek  astronomers 
in  the  time  of  Aristotle  (§  29),  and  probably  much  earlier 
(chapter  I.,  §  17),  though  the  knowledge  was  probably 
confined  to  comparatively  few  people  and  superstitious 
terrors  were  long  associated  with  eclipses. 

The  chief  difficulty  in  dealing  with  eclipses  depends 
on  the  fact  that  the  moon's  path  does  not  coincide 
with  the  ecliptic.  If  the  moon's  path  on  the  celestial 
sphere  were  identical  with  the  ecliptic,  then,  once  every 
month,  at  new  moon,  the  moon  (M)  would  pass  exactly 
between  the  earth  and  the  sun,  and  the  latter  would  be 
eclipsed,  and  once  every  month  also,  at  full  moon,  the 


43] 


Hipparchus 


57 


moon  (M')  would  be  in  the  opposite  direction  to  the  sun 
as  seen  from  the  earth,  and  would  consequently  be  obscured 
by  the  shadow  of  the  earth. 

As,  however,  the  moon's  path  is  inclined  to  the  ecliptic 
(§  40),  the  latitudes  of  the  sun  and  moon  may  differ  by 
as  much  as  5°,  either  when  they  are  in  conjunction,  i.e. 
when  they  have  the  same  longitudes,  or  when  they  are 


FIG.  25. — The  earth's  shadow. 

in  opposition,  i.e.  when  their  longitudes  differ  by  180°, 
and  they  will  then  in  either  case  be  too  far  apart  for  an 
eclipse  to  occur.  Whether  then  at  any  full  or  new  moon 
an  eclipse  will  occur  or  not,  will  depend  primarily  on  the 
latitude  of  the  moon  at  the  time,  and  hence  upon  her 
position  with  respect  to  the  nodes  of  her  orbit  (§  40).  If 
conjunction  takes  place  when  the  sun  and  moon  happen 


N 


S          ECLIPTIC 

FIG.  26. — The  ecliptic  and  the  moon's  path. 


to  be  near  one  of  the  nodes  (N),  as  at  s  M  in  fig.  26,  the 
sun  and  moon  will  be  so  close  together  that  an  eclipse 
will  occur ;  but  if  it  occurs  at  a  considerable  distance  from 
a  node,  as  at  s'  M',  their  centres  are  so  far  apart  that  no 
eclipse  takes  place. 

Now  the  apparent  diameter  of  either  sun  or  moon  is, 
as  we  have  seen  (§  32),  about  |°;  consequently  when  their 
discs  just  touch,  as  in  fig.  27,  the  distance  between  their 
centres  is  also  about  |°.  If  then  at  conjunction  the  dis- 
tance between  their  centres  is  less  than  this  amount,  an 


A  Short  History  of  Astrononiv 


[Cn.  II. 


eclipse  of  the  sun  will  take  place ;  if  not,  there  will  be  no 
eclipse.  It  is  an  easy  calculation  to  determine  (in  fig.  26) 
the  length  of  the  side  N  s  or  N  M  of  the  triangle  N  M  s, 
when  s  M  has  this  value,  and  hence  to 
determine  the  greatest  distance  from  the 
node  at  which  conjunction  can  take  place 
if  an  eclipse  is  to  occur.  An  eclipse  of 
the  moon  can  be  treated  in  the  same  way, 
except  that  we  there  have  to  deal  with  the 
moon  and  the  shadow  of  the  earth  at  the 
distance  of  the  moon.  The  apparent  size 
of  the  shadow  is,  however,  considerably 
greater  than  the  apparent  size  of  the  moon, 
and  an  eclipse  of  the  moon  takes  place  if 
the  distance  between  the  centre  of  the  moon  and  the  centre 
of  the  shadow  is  less  than  about  i°.  As  before,  it  is  easy 
to  compute  the  distance  of  the  moon  or  of  the  centre  of  the 
shadow  from  the  node  when  opposition  occurs,  if  an  eclipse 
just  takes  place.  As,  however,  the  apparent  sizes  of  both 
sun  and  moon,  and  consequently  also  that  of  the  earth's 
shadow,  vary  according  to  the  distances  of  the  sun  and 


FIG.  27. — The  sun 
and  moon. 


FIG.  28.— Partial  eclipse  of 
the  moon. 


FIG.  29.— Total  eclipse  of 
the  moon. 


moon,  a  variation  of  which  Hipparchus  had  no  accurate 
knowledge,  the  calculation  becomes  really  a  good  deal  more 
complicated  than  at  first  sight  appears,  and  was  only  dealt 
with  imperfectly  by  him. 

Eclipses  of  the  moon  are  divided  into  partial  or  total, 
the  former  occurring  when  the  moon  and  the  earth's 
shadow  only  overlap  partially  (as  in  fig.  28),  the  latter 


$  43]  Hipparchus  59 

when  the  moon's  disc  is  completely  immersed  in  the 
shadow  (fig.  29).  In  the  same  way  an  eclipse  of  the  sun 
may  be  partial  or  total ;  but  as  the  sun's  disc  may  be  at 
times  slightly  larger  than  that  of  the  moon,  it  sometimes 
happens  also  that  the  whole  disc  of  the  sun  is  hidden 
by  the  moon,  except  a  narrow  ring  round  the  edge  (as 
in  fig.  30) :  such  an  eclipse  is  called  annular.  As  the 
earth's  shadow  at  the  distance  of  the  moon 
is  always  larger  than  the  moon's  disc,  annular 
eclipses  of  the  moon  cannot  occur. 

Thus  eclipses  take  place  if,  and  only  if, 
the  distance  of  the  moon  from  a  node  at 
the  time  of  conjunction  or  opposition  lies  FlG  -0— Annular 
within  certain  limits  approximately  known  ;  echpse  of  the 
and  the  problem  of  predicting  eclipses  sun. 
could  be  roughly  solved  by  such  knowledge  . 
of  the  motion  of  the  moon  and  of  the  nodes  as  Hipparchus 
possessed.  Moreover,  the  length  of  the  synodic  and 
draconitic  months  (§  40)  being  once  ascertained,  it  became 
merely  a  matter  of  arithmetic  to  compute  one  or  more 
periods  after  which  eclipses  would  recur  nearly  in  the  same 
manner.  For  if  any  period  of  time  contains  an  exact 
number  of  each  kind  of  month,  and  if  at  any  time  an 
eclipse  occurs,  then  after  the  lapse  of  the  period,  con- 
junction (or  opposition)  again  takes  place,  and  the  moon 
is  at  the  same  distance  as  before  from  the  node  and  the 
eclipse  recurs  very  much  as  before.  The  saros,  for  example 
(chapter  i.,  §  17),  contained  very  nearly  223  synodic  or 
242  draconitic  months,  differing  from  either  by  less  than 
an  hour.  Hipparchus  saw  that  this  period  was  not  com- 
pletely reliable  as  a  means  of  predicting  eclipses,  and 
showed  how  to  allow  for  the  irregularities  in  the  moon's 
and  sun's  motion  (§§  39,  40)  which  were  ignored  by  it, 
but  was  unable  to  deal  fully  with  the  difficulties  arising 
from  the  variations  in  the  apparent  diameters  of  the  sun 
or  moon. 

An  important  complication,  however,  arises  in  the  case 
of  eclipses  of  the  sun,  which  had  been  noticed  by  earlier 
writers,  but  which  Hipparchus  was  the  first  to  deal  with. 
Since  an  eclipse  of  the  moon  is  an  actual  darkening  of  the 
moon,  it  is  visible  to  anybody,  wherever  situated,  who  can 


60  A  Short  History  of  Astronomy  [CH.  II. 

see  the  moon  at  all ;  for  example,  to  possible  inhabitants 
of  other  planets,  just  as  we  on  the  earth  can  see  precisely 
similar  eclipses  of  Jupiter's  moons.  An  eclipse  of  the  sun 
is,  however,  merely  the  screening  off  of  the  sun's  light  from 
a  particular  observer,  and  the  sun  may  therefore  be  eclipsed 
to  one  observer  while  to  another  elsewhere  it  is  visible  as 
usual.  Hence  in  computing  an  eclipse  of  the  sun  it  is 
necessary  to  take  into  account  the  position  of  the  observer 
on  the  earth.  The  simplest  way  of  doing  this  is  to  make 
allowance  for  the  difference  of  direction  of  the  moon  as 
seen  by  an  observer  at  the  place  in  question,  and  by  an 
observer  in  some  standard  position  on  the  earth,  preferably 

•M 


FIG.  31. — Parallax 

an.  ideal  observer  at  the  centre  of  the  earth.  If,  in 
fig.  31,  M  denote  the  moon,  c  the  centre  of  the  earth, 
A  a  point  on  the  earth  between  c  and  M  (at  which  therefore 
the  moon  is  overhead),  and  B  any  other  point  on  the  earth, 
then  observers  at  c  (or  A)  and  B  see  the  moon  in  slightly 
different  directions,  c  M,  B  M,  the  difference  between  which 
is  an  angle  known  as  the  parallax,  which  is  equal  to  the 
angle  BMC  and  depends  on  the  distance  of  the  moon, 
the  size  of  the  earth,  and  the  position  of  the  observer 
at  B.  In  the  case  of  the  sun,  owing  to  its  great  distance, 
even  as  estimated  by  the  Greeks,  the  parallax  was  in  all 
cases  too  small  to  be  taken  into  account,  but  in  the  gase 
of  the  moon  the  parallax  might  be  as  much  as  i°  and 
could  not  be  neglected. 


§§  44, 45]  Hipparchus  61 

If  then  the  path  of  the  moon,  as  seen  from  the  centre 
of  the  earth,  were  known,  then  the  path  of  the  moon  as 
seen  from  any  particular  station  on  the  earth  could  be 
deduced  by  allowing  for  parallax,  and  the  conditions  of 
an  eclipse  of  the  sun  visible  there  could  be  computed 
accordingly. 

From  the  time  of  Hipparchus  onwards  lunar  eclipses 
could  easily  be  predicted  to  within  an  hour  or  two  by 
any  ordinary  astronomer ;  solar  eclipses  probably  with  less 
accuracy;  and  in  both  cases  the  prediction  of  the  extent  of 
the  eclipse,  f.e.  of  what  portion  of  the  sun  or  moon  would 
be  obscured,  probably  left  very  much  to  be  desired. 

44.  The  great  services  rendered  to  astronomy  by  Hippar- 
chus can  hardly  be  better  expressed  than  in  the  words  of 
the  great  French  historian  of  astronomy,  Delambre,  who  is 
in  general  no  lenient  critic  of  the  work  of  his  predecessors  : — 

14  When  we  consider  all  that  Hipparchus  invented  or  perfected, 
and  reflect  upon  the  number  of  his  works  and  the  mass  of 
calculations  which  they  imply,  we  must  regard  him  as  one  of 
the  most  astonishing  men  of  antiquity,  and  as  the  greatest  of  all 
in  the  sciences  which  are  not  purely  speculative,  and  which 
require  a  combination  of  geometrical  knowledge  with  a 
knowledge  of  phenomena,  to  be  observed  only  by  diligent 
attention  and  refined  instruments."* 

45.  For  nearly  three  centuries  after  the  death  of  Hippar- 
chus, the  history  of  astronomy  is  almost  a  blank.     Several 
textbooks  written  during  this   period    are  extant,  shewing 
the  gradual  popularisation  of  his  great  discoveries.     Among 
the  few  things  of  interest  in  these  books  may  be  noticed 
a  statement  that  the  stars  are  not  necessarily  on  the  sur- 
face of  a  sphere,  but  may  be  at  different  distances  from 
us,  which,  however,  there  are   no  means  of  estimating ;  a 
conjecture  that  the  sun  and  stars  are  so  far  off  that  the  earth 
would  be  a  mere  point  seen  from  the  sun  and  invisible 
from   the   stars ;    and   a   re-statement   of  an   old   opinion 
traditionally  attributed  to  the  Egyptians  (whether   of  the 
Alexandrine  period  or  earlier  is  uncertain),  that  Venus  and 
Mercury  revolve  round  the  sun.     It  seems  also  that  in  this 
period  some  attempts  were  made  to  explain  the  planetary 

*  Histoire  de  I'Astronotnie  Anctcnne,  Vol.  I.,  p.  185. 


62  A  Short  History  of  Astronomy  [Ca.  n. 

motions  by  means  of  epicycles,  but  whether  these  attempts 
marked  any  advance  on  what  had  been  done  by  Apollonius 
and  Hipparchus  is  uncertain. 

It  is  interesting  also  to  find  in  Pliny  (A.D.  23-79)  tne 
well-known  modern  argument  for  the  spherical  form  of  the 
earth,  that  when  a  ship  sails  away  the  masts,  etc.,  remain 
visible  after  the  hull  has  disappeared  from  view. 

A  new  measurement  of  the  circumference  of  the  earth  by 
Posidonius  (born  about  the  end  of  Hipparchus's  life)  may 
also  be  noticed ;  he  adopted  a  method  similar  to  that  of 
Eratosthenes  (§  36),  and  arrived  at  two  different  results. 
The  later  estimate,  to  which  he  seems  to  have  attached 
most  weight,  was  180,000  stadia,  a  result  which  was  about 
as  much  below  the  truth  as  that  of  Eratosthenes  was 
above  it. 

46.  The  last  great  name  in  Greek  astronomy  is  that 
of  Claudius  Ptolemaeus,  commonly  known  as  Ptolemy^  of 
whose  life  nothing  is  known  except  that  he  lived  in 
Alexandria  about  the  middle  of  the  2nd  century  A.D. 
His  reputation  rests  chiefly  on  his  great  astronomical 
treatise,  known  as  the  Almagest*  which  is  the  source 
from  which  by  far  the  greater  part  of  our  knowledge  of 
Greek  astronomy  is  derived,  and  which  may  be  fairly 
regarded  as  the  astronomical  Bible  of  the  Middle  Ages. 
Several  other  minor  astronomical  and  astrological  treatises 
are  attributed  to  him,  some  of  which  are  probably  not 
genuine,  and  he  was  also  the  author  of  an  important  work 
on  geography,  and  possibly  of  a  treatise  on  Optics,  which 
is,  however,  not  certainly  authentic  and  maybe  of  Arabian 
origin.  The  Optics  discusses,  among  other  topics,  the 
refraction  or  bending  of  light,  by  the  atmosphere  on  the 
earth  :  it  is  pointed  out  that  the  light  of  a  star  or  other 
heavenly  body  s,  on  entering  our  atmosphere  (at  A)  and  on 
penetrating  to  the  lower  and  denser  portions  of  it,  must 
be  gradually  bent  or  refracted,  the  result  being  that  the 

*  The  chief  MS.  bears  the  title  jm.eyd\r]  <rtVra£is,  or  great  composi- 
tion ;though  the  author  refers  to  his  book  elsewhere  as  fj.adr]fji.aTiKrj 
avt>Ta£is  (mathematical  composition).  The  Arabian  translators,  either 
through  admiration  or  carelessness,  converted  peyaK-rj,  great,  into 
/j.eyi<rTr),  greatest,  and  hence  it  became  known  by  the  Arabs  as 
A I  Magisti,  whence  the  Latin  Almagestum  and  our  Almagest. 


46, 47] 


Ptolemy 


star  appears  to  the  observer  at  B  nearer  to  the  zenith  z 
than  it  actually  is,  i.e.  the  light  appears  to  come  from  s' 
instead  of  from  s ;  it  is  shewn  further  that  this  effect  must 
be  greater  for  bodies  near  the  horizon  than  for  those  near 
the  zenith,  the  light  from  the  former  travelling  through 
a  greater  extent  of  atmosphere ;  and  these  results  are 
shewn  to  account  for  certain  observed  deviations  in  the 
daily  paths  of  the  stars,  by  which  they  appear  unduly 
raised  up  when  near  the  horizon.  Refraction  also  explains 
the  well-known  flattened  appearance  of  the  sun  or  moon 
when  rising  or  setting,  the  lower  edge  being  raised  by 


FIG.  32. — Refraction  by  the  atmosphere. 

refraction  more  than  the  upper,  so  that  a  contraction  of 
the  vertical  diameter  results,  the  horizontal  contraction 
being  much  less.* 

47.  The  Almagest  is  avowedly  based  largely  on  the  work 
of  earlier  astronomers,  and  in  particular  on  that  of  Hippar- 
chus,  for  whom  Ptolemy  continually  expresses  the  greatest 
admiration  and  respect.  Many  of  its  contents  have  there- 
fore already  been  dealt  with  by  anticipation,  and  need  not 
be  discussed  again  in  detail.  The  book  plays,  however, 
such  an  important  part  in  astronomical  history,  that  it 
may  be  worth  while  to  give  a  short  outline  of  its  contents, 

*  The  better  known  apparent  enlargement  of  the  sun  or  moon 
when  rising  or  setting  has  nothing  to  do  with  refraction.  It  is  an 
optical  illusion  not  very  satisfactorily  explained,  but  probably  due  to 
the  lesser  brilliancy  of  the  sun  at  the  time. 


64  A  Short  History  of  Astronomy  [Cn.  n. 

tn  addition  to  dealing  more  fully  with  the  parts  in  which 
Ptolemy  made  important  advances. 

The  Almagest  consists  altogether  of  13  books.  The 
first  two  deal  with  the  simpler  observed  facts,  such  as  the 
daily  motion  of  the  celestial  sphere,  and  the  general 
motions  of  the  sun,  moon,  and  planets,  and  also  with  a 
number  of  topics  connected  with  the  celestial  sphere  and 
its  motion,  such  as  the  length  of  the  day  and  the  times 
of  rising  and  setting  of  the  stars  in  different  zones  of  the 
earth  ;  there  are  also  given  the  solutions  of  some  important 
mathematical  problems,*  and  a  mathematical  tablet  of 
considerable  accuracy  and  extent.  But  the  most  interest- 
ing parts  of  these  introductory  books  deal  with  what  may 
be  called  the  postulates  of  Ptolemy's  astronomy  (Book  I., 
chap.  ii.).  The  first  of  these  is  that  the  earth  is  spherical; 
Ptolemy  discusses  and  rejects  various  alternative  views, 
and  gives  several  of  the  usual  positive  arguments  for  a 
spherical  form,  omitting,  however,  one  of  the  strongest, 
the  eclipse  argument  found  in  Aristotle  (§  29),  possibly 
as  being  too  recondite  and  difficult,  and  adding  the 
argument  based  on  the  increase  in  the  area  of  the  earth 
visible  when  the  observer  ascends  to  a  height.  In  his 
geography  he  accepts  the  estimate  given  by  Posidonius 
that  the  circumference  of  the  earth  is  i8o,oo«  stadia.  The 
other  postulates  which  he  enunciates  and  for  which  he 
argues  are,  that  the  heavens  are  spherical  and  revolve  like 
a  sphere ;  that  the  earth  is  in  the  centre  of  the  heavens, 
and  is  merely  a  point  in  comparison  with  the  distance  of 
the  fixed  stars,  and  that  it  has  no  motion.  The  position 
of  these  postulates  in  the  treatise  and  Ptolemy's  general 
method  of  procedure  suggest  that  he  was  treating  them,  not 
so  much  as  important  results  to  be  established  by  the  best 
possible  evidence,  but  rather  as  assumptions,  more  pro- 
bable than  any  others  with  which  the  author  was  acquainted, 
on  which  to  base  mathematical  calculations  which  should 
explain  observed  phenomena.*  His  attitude  is  thus 

*  In  spherical  trigonometry. 

f  A  table  of  chords  (or  double  sines  of  half-angles)  for  every  ^° 
from  o°  to  1 80°. 

J  His  procedure  may  be  compared  with  that  of  a  political 
economist  of  the  school  of  Ricardo,  who,  in  order  to  establish  some 


$  48]  The  Almagest  65 

essentially  different  from  that  either  of  the  early  Greeks, 
such  as  Pythagoras,  or  of  the  controversialists  of  the  i6th 
and  early  i;th  centuries,  such  as  Galilei  (chapter  vi.),  for 
whom  the  truth  or  falsity  of  postulates  analogous  to  those 
of  Ptolemy  was  of  the  very  essence  of  astronomy  and  was 
among  the  final  objects  of  inquiry.  The  arguments  which 
Ptolemy  produces  in  support  of  his  postulates,  arguments 
which  were  probably  the  commonplaces  of  the  astronomical 
writing  of  his  time,  appear  to  us,  except  in  the  case  of 
the  shape  of  the  earth,  loose  and  of  no  great  value. 
The  other  postulates  were,  in  fact,  scarcely  capable  of 
either  proof  or  disproof  with  the  evidence  which  Ptolemy 
had  at  command.  His  argument  in  favour  of  the  immo- 
bility of  the  earth  is  interesting,  as  it  shews  his  clear 
perception  that  the  more  obvious  appearances  can  be 
explained  equally  well  by  a  motion  of  the  stars  or  by  a 
motion  of  the  earth ;  he  concludes,  however,  that  it  is 
easier  to  attribute  motion  to  bodies  like  the  stars  which 
seem  to  be  of  the  nature  of  fire  than  to  the  solid  earth, 
and  points  out  also  the  difficulty  of  conceiving  the  earth  to 
have  a  rapid  motion  of  which  we  are  entirely  unconscious. 
He  does  not,  however,  discuss  seriously  the  possibility  that 
the  earth  or  even  Venus  and  Mercury  may  revolve  round 
the  sun. 

The  third  book  of  the  Almagest  deals  with  the  length  of 
the  year  and  theory  of  the  sun,  but  adds  nothing  of  import- 
ance to  the  work  of  Hipparchus 

48.  The  fourth  book  of  the  Almagest,  which  treats  of 
the  length  of  the  month  and  of  the  theory  of  the  moon, 
contains  one  of  Ptolemy's  most  important  discoveries.  We 
have  seen  that,  apart  from  the  motion  of  the  moon's  orbit 
as  a  whole,  and  the  revolution  of  the  line  of  apses,  the 
chief  irregularity  or  inequality  was  the  so-called  equation 
of  the  centre  (§§  39,  40),  represented  fairly  accurately  by 

rough  explanation  of  economic  phenomena,  starts  with  certain  simple 
assumptions  as  to  human  nature,  which  at  any  rate  are  more  plausible 
than  any  other  equally  simple  set,  and  deduces  from  them  a  number 
of  abstract  conclusions,  the  applicability  ot  which  to  real  life  has 
to  be  considered  in  individual  cases.  But  the  perfunctory  discussion 
which  such  a  writer  gives  ot  the  qualities  of  the  "economic  man" 
cannot  of  course  be  regarded  as  his  deliberate  and  final  estimate 
of  human  nature. 


66  A  Short  History  of  Astronomy  [Cu.  IL 

means  of  an  eccentric,  and  depending  only  on  the  position 
of  the  moon  with  respect  to  its  apogee.  Ptolemy,  however, 
discovered,  what  Hipparchus  only  suspected,  that  there 
was  a  further  inequality  in  the  moon's  motion — to  which 
the  name  evection  was  afterwards  given —  and  that  this 
depended  partly  on  its  position  with  respect  to  the  sun. 
Ptolemy  compared  the  observed  positions  of  the  moon  with 
those  calculated  by  Hipparchus  in  various  positions  relative 
to  the  sun  and  apogee,  and  found  that,  although  there  was 
a  satisfactory  agreement  at  new  and  full  moon,  there  was  a 
considerable  error  when  the  moon  was  half-full,  provided 
it  was  also  not  very  near  perigee  or  apogee.  ^Hipparchus 
based  his  theory  of  the  moon  chiefly  on  observations  of 
eclipses,  i.e.  on  observations  taken  necessarily  at  full  or  new 
moon  (§  43),  and  Ptolemy's  discovery  is  due  to  the  fact 
that  he  checked  Hipparchus's  theory  by  observations  taken 
at  other  times.  To  represent  this  new  inequality,  it  was 
found  necessary  to  use  an  epicycle  and  a  deferent,  the  latter 
being  itself  a  moving  eccentric  circle,  the  centre  of  which 
revolved  round  the  earth.  To  account,  to  some  extent,  for 
certain  remaining  discrepancies  between  theory  and  obser- 
vation, which  occurred  neither  at  new  and  full  moon,  nor 
at  the  quadratures  (half-moon),  Ptolemy  introduced  further 
a  certain  small  to-and-fro  oscillation  of  the  epicycle,  an 
oscillation  to  which  he  .gave  the  name  of  prosneusis.* 

*  The  equation  of  the  centre  and  the  evection  may  be  expressed 
trigonometrically  by  two  terms  in  the  expression  for  the  moon's 
longitude,  a  sin  0  +  b  sin  (2  0  -  6),  where  a,  b  are  two  numerical 
quantities,  in  round  numbers  6°  and  1°,  6  is  the  angular  distance  of 
the  moon  from  perigee,  and  0  is  the  angular  distance  from  the  sun. 
At  conjunction  and  opposition  0  is  o°  or  180°,  and  the  two  terms 
reduce  to  (a—b)  sin  6.  This  would  be  the  form  in  which  the 
equation  of  the  centre  would  have  presented  itself  to  Hipparchus. 
Ptolemy's  correction  is  therefore  equivalent  to  adding  on 

b  [sin  6  +  sin  (2  0  —  0)],  or  2  b  sin  <p  cos  (0—0), 

which  vanishes  at  conjunction  or  opposition,  but  reduces  at  the 
quadratures  to  2  b  sin  0,  which  again  vanishes  if  the  moon  is  at  apogee 
or  perigee  (6  =  o°  or  180°),  but  has  its  greatest  value  half-way 
between,  when  6  =  90°.  Ptolemy's  construction  gave  rise  also  to 
a  still  smaller  term  of  the  type, 

csin  2  0  [cos  (204    0)  +  2  cos  (2  0  —  0)], 

which,  it  will  be  observed,  vanishes  at  quadratures  as  well  as  at 
conjunction  and  opposition. 


5  49]  The  Almagest  67 

Ptolemy  thus  succeeded  in  fitting  his  theory  on  to  his 
observations  so  well  that  the  error  seldom  exceeded  10', 
a  small  quantity  in  the  astronomy  of  the  time,  and  on 
the  basis  of  this  construction  he  calculated  tables  from 
which  the  position  of  the  moon  at  any  required  time  could 
be  easily  deduced. 

One  of  the  inherent  weaknesses  of  the  system  of  epi- 
cycles occurred  in  this  theory  in  an  aggravated  form.  It 
has  already  been  noticed  in  connection  with  the  theory  of 
the  sun  (§  39),  that  the  eccentric  or  epicycle  produced  an 
erroneous  variation  in  the  distance  of  the  sun,  which  was, 
however,  imperceptible  in  Greek  times.  Ptolemy's  system, 
however,  represented  the  moon  as  being  sometimes  nearly 
twice  as  far  off  as  at  others,  and  consequently  the  apparent 
diameter  ought  at  some  times  to  have  been  not  much  more 
than  half  as  great  as  at  others — a  conclusion  obviously 
inconsistent  with  observation.  It  seems  probable  that 
Ptolemy  noticed  this  difficulty,  but  was  unable  to  deal  with 
it;  it  is  at  any  rate  a  significant  fact  that  when  he  is  dealing 
with  eclipses,  for  which  the  apparent  diameters  of  the  sun 
and  moon  are  of  importance,  he  entirely  rejects  the  estimates 
that  might  have  been  obtained  from  his  lunar  theory  and 
appeals  to  direct  observation  (cf.  also  §  51,  note). 

49.  The  fifth  book  of  the  Almagest  contains  an  account 
of  the  construction  and  use  of  Ptolemy's  chief  astronomical 
instrument,  a  combination  of  graduated  circles  known  as 
the  astrolabe.* 

Then  follows  a  detailed  discussion  of  the  moon's 
parallax  (§  43),  and  of  the  distances  of  the  sun  and  moon. 
Ptolemy  obtains  the  distance  of  the  moon  by  a  parallax 
method  which  is  substantially  identical  with  that  still  in  use. 
If  we  know  the  direction  of  the  line  c  M  (fig.  33)  joining  the 
centres  of  the  earth  and  moon,  or  the  direction  of  the 
moon  as  sten  by  an  observer  at  A;  and  also  the  direction 
of  the  line  B  M,  that  is  the  direction  of  the  moon  as  seen 
by  an  observer  at  B,  then  the  angles  of  the  triangle  c  B  M 
are  known,  and  the  ratio  of  the  sides  c  B,  c  M  is  known. 

*  Here,  as  elsewhere,  I  have  given  no  detailed  account  of  astro- 
nomical instruments,  believing  such  descriptions  to  be  in  general 
neither  interesting  nor  intelligible  to  those  who  have  not  the  actual 
instruments  before  them,  and  to  be  of  little  use  to  those  who  have. 


68  A  Short  History  of  Astronomy  [CH.  II. 

Ptolemy  obtained  the  two  directions  required  by  means 
of  observations  of  the  moon,  and  hence  found  that  c  M 
was  59  times  c  B,  or  that  the  distance  of  the  moon  was 
equal  to  59  times  the  radius  of  the  earth.  He  then  uses 
Hipparchus's  eclipse  method  to  deduce  the  distance  of  the 
sun  from  that  of  the  moon  thus  ascertained,  and  finds 
the  distance  of  the  sun  to  be  1,210  times  the  radius  of 
the  earth.  This  number,  which  is  substantially  the  same 
as  that  obtained  by  Hipparchus  (§  41),  is,  however,  only 

•M 


FIG.  33. — Parallax. 

about  -gV  of  the  true  number,  as  indicated  by  modern 
work  (chapter  xm.,  §  284). 

The  sixth  book  is  devoted  to  eclipses,  and  contains  no 
substantial  additions  to  the  work  of  Hipparchus. 

50.  The  seventh  and  eighth  books  contain  a  catalogue  of 
stars,  and  a  discussion  of  precession  (§  42).  The  catalogue, 
which  contains  1,028  stars  (three  of  which  are  duplicates), 
appears  to  be  nearly  identical  with  that  of  Hipparchus. 
It  contains  none  of  the  stars  which  were  visible  to  Ptolemy 
at  Alexandria,  but  not  to  Hipparchus  at  Rhodes.  More- 
over, Ptolemy  professes  to  deduce  from  a  comparison  of 
his  observations  with  those  of  Hipparchus  and  others  the 
(erroneous)  value  36"  for  the  precession,  which  Hipparchus 
had  given  as  the  least  possible  value,  and  which  Ptolemy 
regards  as  his  final  estimate.  But  an  examination  of 


$$  so,  si]  The  Almagest  69 

the  positions  assigned  to  the  stars  in  Ptolemy's  catalogue 
agrees  better  with  their  actual  positions  in  the  time  of 
Hipparchus,  corrected  for  precession  at  the  supposed  rate  of 
36"  annually,  than  with  their  actual  positions  in  Ptolemy's 
time.  It  is  therefore  probable  that  the  catalogue  as  a 
whole  does  not  represent  genuine  observations  made  by 
Ptolemy,  but  is  substantially  the  catalogue  of  Hipparchus 
corrected  for  precession  and  only  occasionally  modified  by 
new  observations  by  Ptolemy  or  others. 

51.  The  last  five  Jpooks  deal  with  the  theory  of  the 
planets,  the  most  important  of  Ptolemy's  original  contribu- 
tions to  astronomy.  The  problem  of  giving  a  satisfactory 
explanation  of  the  motions  of  the  planets  was,  on  account 
of  their  far  greater  irregularity,  a  much  more  difficult  one 
than  the  corresponding  problem  for  the  sun  or  moon.  The 
motions  of  Ihe  latter  are  so  nearly  uniform  that  their 
irregularities  may  usually  be  regarded  as  of  the  nature  of 
small  corrections,  and  for  many  purposes  may  be  ignored. 
The  planets,  however,  as  we  have  seen  (chapter  i.,  §  14),  do 
not  even  always  move  from  west  to  east,  but  stop  at  intervals, 
move  in  the  reverse  direction  for  a  time,  stop  again,  and 
then  move  again  in  the  original  direction.  It  was  probably 
recognised  in  early  times,  at  latest  by  Eudoxus  (§  26),  that 
in  the  case  of  three  of  the  planets,  Mars,  Jupiter,  and  Saturn, 
these  motions  could  be  represented  roughly  by  supposing 
each  planet  to  oscillate  to  and  fro  on  each  side  of  a  fictitious 
planet,  moving  uniformly  round  the  celestial  sphere  in  or 
near  the  ecliptic,  and  that  Venus  and  Mercury  could 
similarly  be  regarded  as  oscillating  to  and  fro  on  each  side 
of  the  sun.  These  rough  motions  could  easily  be  inter- 
preted by  means  of  revolving  spheres  or  of  epicycles,  as  was 
done  by  Eudoxus  and  probably  again  with  more  precision 
by  Apollonius.  In  the  case  of  Jupiter,  for  example,  we 
may  regard  the  planet  as  moving  on  an  epicycle,  the  centre 
of  which,  /,  describes  uniformly  a  deferent,  the  centre  of 
which  is  the  earth.  The  planet  will  then  as  seen  from  the 
earth  appear  alternately  to  the  east  (as  at  jj)  and  to  the 
west  (as  at  j.,)  of  the  fictitious  planet/;  and  the  extent  of 
the  oscillation  on  each  side,  and  the  interval  between  suc- 
cessive appearances  in  the  extreme  positions  (jlf  J2)  on  either 
side,  can  be  made  right  by  choosing  appropriately  the  size 


A  Short  History  of  Astronomy 


[CH.   II. 


and  rapidity  of  motion  of  the  epicycle.  It  is  moreover 
evident  that  with  this  arrangement  the  apparent  motion 
of  Jupiter  will  vary  considerably,  as  the  two  motions — that 
on  the  epicycle  and  that  of  the  centre  of  the  epicycle  on 
the  deferent — are  sometimes  in  the  same  direction,  so  as 
to  increase  one  another's  effect,  and  at  other  times  in 
opposite  directions.  Thus,  when  Jupiter  is  most  distant 
from  the  earth,  that  is  at  J3,  the  motion  is  most  rapid,  at 
]l  and  J2  the  motion  as  seen  from  the  earth  is  nearly  the 
same  as  that  of  j  j  while  at  J4  the  two  motions  are  in 

opposite  directions,  and  the 
size  and  motion  of  the  epi- 
cycle having  been  chosen  in 
the  way  indicated  above, 
it  is  found  in  fact  that  the 
motion  of  the  planet  in  the 
epicycle  is  the  greater  of  the 
two  motions,  and  that  there- 
fore the  planet  when  in 
this  position  appears  to  be 
moving  from  east  to  west 
(from  left  to  right  in  the 
figure),  as  is  actually  the 
case.  As  then  at  ji  and 
J2  the  planet  appears  to 
be  moving  from  west  to 

east,  and  at  J4  in  the  opposite  direction,  and  sudden 
changes  of  motion  do  not  occur  in  astronomy,  there  must 
be  a  position  between  jt  and  J4,  and  another  between 
J4  and  J2,  at  which  the  planet  is  just  reversing  its  direction 
of  motion,  and  therefore  appears  for  the  instant  at  rest. 
We  thus  arrive  at  an  explanation  of  the  stationary  points 
(chapter  I.,  §  14).  An  exactly  similar  scheme  explains 
roughly  the  motion  of  Mercury  and  Venus,  except  that 
the  centre  of  the  epicycle  must  always  be  in  the  direction 
of  the  sun. 

Hipparchus,  as  we  have  seen  (§41),  found  the  current 
representations  of  the  planetary  motions  inaccurate,  and 
collected  a  number  of  fresh  observations.  These,  with 
fresh  observations  of  his  own,  Ptolemy  now  employed 
in  order  to  construct  an  improved  planetary  system. 


FIG.  34. — Jupiter's  epicycle 
and  deferent. 


Si] 


The  Almagest 


7 


As  in  the  case  of  the  moon,  he  used  as  deferent  an 
eccentric  circle  (centre  c),  hut  instead  of  making  the 
centre  j  of  the  epicycle  move  uniformly  in  the  deferent,  he 
introduced  a  new  point  called  an  equant  (E'),  situated  at 
the  same  distance  from  the  centre  of  the  deferent  as  the 
earth  but  on  the  opposite  side,  and  regulated  the  motion  of 
j  by  the  condition  that  the  apparent  motion  as  seen  from  the 
equant  should  be  uniform;  in  other  words,  the  angle  A  E' j 
was  made  to  increase  uniformly.  In  the  case  of  Mercury 
(the  motions  of  which  have  been  found  troublesome  by 
astronomers  of  all  periods), 
the  relation  of  the  equant  to 
the  centre  of  the  epicycle  was 
different,  and  the  latter  was 
made  to  move  in  a  small 
circle.  The  deviations  of  the 
planets  from  the  ecliptic 
(chapter  i.,  §§  13,  14)  were 
accounted  for  by  tilting  up 
the  planes  of  the  several 
deferents  arid  epicycles  so 
that  they  were  inclined  to  the 
ecliptic  at  various  small  angles. 

By  means  of  a  system  of  this 
kind,  worked   out  with  great 

care,  and  evidently  at  the  cost  of  enormous  labour,  Ptolemy 
was  able  to  represent  with  very  fair  exactitude  the  motions 
of  the  planets,  as  given  by  the  observations  in  his  possession. 

It  has  been  pointed  out  by  modern  critics,  as  well  as  by 
some  mediaeval  writers,  that  the  use  of  the  equant  (which 
played  also  a  small  part  in  Ptolemy's  lunar  theory)  was  a 
violation  of  the  principle  of  employing  only  uniform  circular 
motions,  on  which  the  systems  of  Hipparchus  and  Ptolemy 
were  supposed  to  be  based,  and  that  Ptolemy  himself 
appeared  unconscious  of  his  inconsistency.  It  may,  how- 
ever, fairly  be  doubted  whether  Hipparchus  or  Ptolemy 
ever  had  an  abstract  belief  in  the  exclusive  virtue  of  such 
motions,  except  as  a  convenient  and  easily  intelligible 
way  of  representing  certain  more  complicated  motions, 
and  it  is  difficult  to  conceive  that  Hipparchus  would  have 
scrupled  any  more  than  his  great  follower,  in  using  an 


FIG.  35. —  1  he  equant. 


72  A  Short  History  of  Astronomy  [Cn.  n. 

equant  to  represent  an  irregular  motion,  if  he  had  found 
that  the  motion  was  thereby  represented  with  accuracy. 
The  criticism  appears  to  me  in  fact  to  be  an  anachronism. 
The  earlier  Greeks,  whose  astronomy  was  speculative  rather 
than  scientific,  and  again  many  astronomers  of  the  Middle 
Ages,  felt  that  it  was  on  a  priori  grounds  necessary  to  re- 
present the  "perfection"  of  the  heavenly  motions  by  the 
most  "  perfect "  or  regular  of  geometrical  schemes ;  so  that 
it  is  highly  probable  that  Pythagoras  or  Plato,  or  even 
Aristotle,  would  have  objected,  and  certain  that  the 
astronomers  of  the  i4th  and  i5th  centuries  ought  to  have 
objected  (as  some  of  them  actually  did),  to  this  innova- 
tion of  Ptolemy's.  But  there  seems  no  good  reason  fox 
attributing  this  a  priori  attitude  to  the  later  scientific  Greek 
astronomers  (cf.  also  §§  38,  47).* 

It  will  be  noticed  that  nothing  has  been  said  as  to  the 
actual  distances  of  the  planets,  and  in  fact  the  apparent 
motions  are  unaffected  by  any  alteration  in  the  scale  on 
which  deferent  and  epicycle  are  constructed,  provided  that 
both  are  altered  proportionally.  Ptolemy  expressly  states  that 
he  had  no  means  of  estimating  numerically  the  distances  of 
the  planets,  or  even  of  knowing  the  order  of  the  distance  of 
the  several  planets.  He  followed  tradition  in  accepting 
conjecturally  rapidity  of  motion  as  a  test  of  nearness,  and 
placed  Mars,  Jupiter,  Saturn  (which  perform  the  circuit 
of  the  celestial  sphere  in  about  2,  12,  and  29  years  re- 
spectively) beyond  the  sun  in  that  order.  As  Venus  and 

*  The  advantage  derived  from  the  use  of  the  equant  can  be  made 
clearer  by  a  mathematical  comparison  with  the  elliptic  motion  in- 
troduced by  Kepler.  In  elliptic  motion  the  angular  motion  and 
distance  are  represented  approximately  by  the  formulae  nt  +  2e  sin  nt. 
a  (l  —  e  cos  nf)  respectively;  the  corresponding  formulae  given  by 
the  use  of  the  simple  eccentric  are  nt  +  e'  sin  nt,  a  (l  —  e'  cos  nt). 
To  make  the  angular  motions  agree  we  must  therefore  take  e'  =  2e, 
but  to  make  the  distances  agree  we  must  take  e'  =  e't  the  two  con- 
ditions are  therefore  inconsistent.  But  by  the  introduction  of  an 
equant  the  formulae  become  nt  +  2e'  sin  nt,  a  (l  —  e'  cos  nf),  and 
both  agree  if  we  take  e'  =  e.  Ptolemy's  lunar  theory  could  have 
been  nearly  freed  from  the  serious  difficulty  already  noticed  (§  48^ 
if  he  had  used  an  equant  to  represent  the  chief  inequality  of  the 
moon ;  and  his  planetary  theory  would  have  been  made  accurate 
to  the  first  order  of  small  quantities  by  the  use  of  an  equant  both 
for  the  deferent  and  the  epicycle. 


$$  52,  53]  Ptolemy  and  his  Successors  73 

Mercury  accompany  the  sun,  and  may  therefore  be  regarded 
as  on  the  average  performing  their  revolutions  in  a  y^ar, 
the  test  to  some  extent  failed  in  their  case,  but  Ptolemy 
again  accepted  the  opinion  of  the  "  ancient  mathematicians  " 
(i.e.  probably  the  Chaldaeans)  that  Mercury  and  Venus  lie 
between  the  sun  and  moon,  Mercury  being  the  nearer  to 
us.  (Cf.  chapter  i.,  §  15.) 

52.  There  has  been  much  difference  of  opinion  among 
astronomers  as  to  the  merits  of  Ptolemy.     Throughout  the 
Middle  Ages  his  authority  was  regarded  as  almost  final  on 
astronomical  matters,  except  where  it  was  outweighed  by 
the  even  greater  authority  assigned  to  Aristotle.     Modern 
criticism  has  made  clear,  a  fact  which  indeed  he  never 
conceals,  that  his  work  is  to  a  large  extent  based  on  that 
of  Hipparchus  ;  and  that  his  observations,  if  not  actually 
fictitious,  were  at  any  rate  in  most  cases  poor.      On  the 
other  hand  his  work  shews  clearly  that  he  was  an  accom- 
plished and  original  mathematician.*     The  most  important 
of  his  positive  contributions  to  astronomy  were  the  discovery 
of  evection  and  his  planetary  theory,  but  we  ought  probably 
to  rank  above  these,  important  as  they  are,  the  services 
which  he  rendered  by  preserving  and  developing  the  great 
ideas  of  Hipparchus — ideas  which  the  other  astronomers 
of  the  time  were  probably  incapable  of  appreciating,  and 
which  might  easily  have  been  lost  to  us  if  they  had  not 
been  embodied  in  the  Almagest. 

53.  The  history  of  Greek  astronomy  practically  ceases 
with  Ptolemy.     The  practice  of  observation   died   out  so 
completely  that  only  eight  observations  are  known  to  have 
been  made  during  the  eight  and   a  half  centuries  which 
separate  him  from   Albategnius  (chapter  HI.,  §  59).     The 
onlv  Greek  writers  after  Ptolemy's  time  are  compilers  and 
commentators,  such   as   Theon  (fl.  A.D.   365),  to    none  of 
whom  original  ideas  of  any  importance  can  be  attributed. 
The  murder  of  his  daughter  Hypatia  (A.D.  415),  herself 
also  a  writer  on  astronomy,  marks  an  epoch  in  the  decay 
of  the  Alexandrine  school ;  and  the  end  came  in  A.D.  640, 
when  Alexandria  was  captured  by  the  Arabs. t 

*  De  Morgan  classes  him  as  a  geometer  with  Archimedes,  Euclid, 
and  Apollonius,  the  three  great  geometers  of  antiquity. 

j-  The  legend  that  the  books  in  the  library  served  for  six  months  as 


74  A  Short  History  of  Astronomy  [CH.  n. 

54.  It  remains  to  attempt  to  estimate  briefly  the  value  of 
the  contributions  to  astronomy  made  by  the  Greeks  and  of 
their  method  of  investigation.  It  is  obviously  unreasonable 
to  expect  to  find  a  brief  formula  which  will  characterise  the 
scientific  attitude  of  a  series  of  astronomers  whose  lives 
extend  over  a  period  of  eight  centuries  ;  and  it  is  futile 
to  explain  the  inferiority  of  Greek  astronomy  to  our  own  on 
some  such  ground  as  that  they  had  not  discovered  the  method 
of  induction,  that  they  were  not  careful  enough  to  obtain 
facts,  or  even  that  their  ideas  were  not  clear.  In  habits 
of  thought  and  scientific  aims  the  contrast  between  Pytha- 
goras and  Hipparchus  is  probably  greater  than  that  between 
Hipparchus  on  the  one  hand  and  Coppernictis  or  even 
Newton  on  the  other,  while  it  is  not  unfair  to  say  that  the 
fanciful  ideas  which  pervade  the  work  of  even  so  great  a 
discoverer  as  Kepler  (chapter  vii.,  §§  144,  151)  place  his 
scientific  method  in  some  respects  behind  that  of  his  great 
Greek  predecessor. 

The  Greeks  inherited  from  their  predecessors  a  number 
of  observations,  many  of  them  executed  with  considerable 
accuracy,  which  were  nearly  sufficient  for  the  requirements 
of  practical  life,  but  in  the  matter  of  astronomical  theory 
and  speculation,  in  which  their  best  thinkers  were  very 
much  more  interested  than  in  the  detailed  facts,  they 
received  virtually  a  blank  sheet  on  which  they  had  to  write 
(at  first  with  indifferent  success)  their  speculative  ideas. 
A  considerable  interval  of  time  was  obviously  necessary  to 
bridge  over  the  gulf  separating  such  data  as  the  eclipse 
observations  of  the  Chaldaeans  from  such  ideas  as  the 
harmonical  spheres  of  Pythagoras ;  and  the  necessary 
theoretical  structure  could  not  be  erected  without  the  use 
of  mathematical  methods  which  had  gradually  to  be  in- 
vented. That  the  Greeks,  particularly  in  early  times,  paid 
little  attention  to  making  observations,  is  true  enough,  but 
it  may  fairly  be  doubted  whether  the  collection  of  fresh 
material  for  observations  would  really  have  carried 
astronomy  much  beyond  the  point  reached  by  the 
Chaldaean  observers.  When  once  speculative  ideas,  made 

fuel  for  the  furnaces  of  the  public  baths  is  rejected  by  Gibbon  and 
others.  One  good  reason  for  not  accepting  it  is  that  by  this  time 
there  were  probably  very  few  books  left  to  burn. 


$  54]  Estimate  of  Greek  Astronomy  75 

definite  by  the  aid  of  geometry,  had  been  sufficiently 
developed  to  be  capable  of  comparison  with  observation, 
rapid  progress  was  made.  The  Greek  astronomers  of  the 
scientific  period,  such  as  Aristarchus,  Eratosthenes,  and 
above  all  Hipparchus,  appear  moreover  to  have  followed 
in  their  researches  the  method  which  has  always  been 
fruitful  in  physical  science — namely,  to  frame  provisional 
hypotheses,  to  deduce  their  mathematical  consequences, 
and  to  compare  these  with  the  results  of  observation. 
There  are  few  better  illustrations  of  genuine  scientific 
caution  than  the  way  in  which  Hipparchus,  having  tested 
the  planetary  theories  handed  down  to  him  and  having 
discovered  their  insufficiency,  deliberately  abstained  from 
building  up  a  new  theory  on  data  which  he  knew  to  be 
insufficient,  and  patiently  collected  fresh  material,  never  to 
be  used  by  himself,  that  some  future  astronomer  might 
thereby  be  able  to  arrive  at  an  improved  theory. 

Of  positive  additions  to  our  astronomical  knowledge 
made  by  the  Greeks  the  most  striking  in  some  ways  is  the 
discovery  of  the  approximately  spherical  form  of  the  earth, 
a  result  which  later  work  has  only  slightly  modified.  But 
their  explanation  of  the  chief  motions  of  the  solar  system 
and  their  resolution  of  them  into  a  comparatively  small 
number  of  simpler  motions  was,  in  reality,  a  far  more  im- 
portant contribution,  though  the  Greek  epicyclic  scheme 
has  been  so  remodelled,  that  at  first  sight  it  is  difficult  to 
recognise  the  relation  between  it  and  our  modern  views. 
The  subsequent  history  will,  however,  show  how  completely 
each  stage  in  the  progress  of  astronomical  science  has 
depended  on  those  that  preceded. 

When  we  study  the  great  conflict  in  the  time  of  Copper- 
nicus  between  the  ancient  and  modern  ideas,  our  sympathies 
naturally  go  out  towards  those  who  supported  the  latter, 
which  are  now  known  to  be  more  accurate,  and  we  are  apt  to 
forget  that  those  who  then  spoke  in  the  name  of  the  ancient 
astronomy  and  quoted  Ptolemy  were  indeed  believers  in 
the  doctrines  which  they  had  derived  from  the  Greeks,  but 
that  their  methods  of  thought,  their  frequent  refusal  to  face 
facts,  and  their  appeals  to  authority,  were  all  entirely 
foreign  to  the  spirit  of  the  great  men  whose  disciples  they 
believed  themselves  to  be. 


CHAPTER    III. 

THE      MIDDLE      AGES. 

"The  lamp  burns  low,  and  through  the  casement  bars 
Grey  morning  glimmers  feebly." 

BROWNING'S  Paracelsus. 

55.  ABOUT  fourteen  centuries  elapsed  between  the  publica- 
'   tion  of  the  Almagest  and  the  death  of  Coppernicus  (1543), 
|    a  date  which  is  in  astronomy  a  convenient  landmark  on  the 
\  boundary  between  the  Middle  Ages  and  the  modern  world. 
I   In  this  period,  nearly  twice  as  long  as  that  which  separated 
Thales  from  Ptolemy,  almost  four   times   as  long  as  that 
/    which  has  now  elapsed  since  the  death  of  Coppernicus,  no 
\    astronomteaj^iiscayery  of  first-rate  importance  was  made. 
THefe"were  some  importanniavarnces  in  mathematics,  and 
the    art    of    observation   was    improved ;   but    theoretical 
astronomy  made  scarcely  any  progress,  and  in  some  respects 
even  went   backward,   the   current   doctrines,    if  in   some 
points  slightly  more  correct  than  those  of  Ptolemy,  being 
v  Jess  intelligently  held. 

In  the  Western  World  we  have  already  seen  that  there 
was  little  to  record  for  nearly  five  centuries  after  Ptolemy. 
After  that  time  ensued  an  almost  total  blank,  and  several 
more  centuries  elapsed  before  there  was  any  appreciable 
revival  of  the  interest  once  felt  in  astronomy. 

56.  Meanwhile  a  remarkable  development  of  science  had 
taken  place  in  the  East  during  the  yth  century.  The 
descendants  of  the  wild  Arabs  who  had  carried  the  banner 
of  Mahomet  over  so  large  a  part  of  the  Roman  empire,  as 
well  as  over  lands  lying  farther  east,  soon  began  to  feel  the 
influence  of  the  civilisation  of  the/\peoples  whom  they  had 
subjugated,  and^gagdad,  which  m  the  8th  century  became 

76 


CH.  in.,  w  55, 5o  The  Bagdad  School  77 

the  capital  of  the  Caliphs,  rapidly  developed  into  a  centre  of 
literary  and  scientific  activity.  Al  Mansur,  who  reigned 
from  A.D.  754  to  775,  was  noted  as  a  patron  of  science, 
and  collected  round  him  learned  men  both  from  India  and 
the  West.  In  particular  we  are  told  of  the  arrival  at  his 
court  in  772  of  a  scholar  from  India  bearing  with  him  an 
Indian  treatise  on  astronomy,*  which  was  translated  into 
Arabic  by  order  of  the  Caliph,  and  remained  the  standard 
treatise  for  nearly  half  a  century.  From  Al  Mansur's  time 
onwards  a  body  of  scholars,  in  the  first  instance  chiefly 
Syrian  Christians,  were  at  work  at  the  court  of  the  Caliphs 
translating  Greek  writings,  often  through  the  medium  of 
Syriac,  into  Arabic.  The  first  translations  made  were  of 
the  medical  treatises  of  Hippocrates  and  Galen ;  the 
Aristotelian  ideas  contained  in  the  latter  appear  to  have 
stimulated  interest  in  the  writings  of  Aristotle  himself,  and 
thus  to  have  enlarged  the  range  of  subjects  regarded  as 
worthy  of  study.  Astronomy  soon  followed  medicine,  and 
became  the  favourite  science  of  the  Arabians,  partly  no  doubt 
out  of  genuine  scientific  interest,  but  probably  still  more  for 
the  sake  of  its  practical  applications.  Certain  Mahometan 
ceremonial  observances  required  a  knowledge  of  the 
direction  of  Mecca,  and  though  many  worshippers,  living 
anywhere  between  the  Indus  and  the  Straits  of  Gibraltar, 
must  have  satisfied  themselves  with  rough-and-ready 
solutions  of  this  problem,  the  assistance  which  astronomy 
could  give  in  fixing  the  true  direction  was  welcome  in 
larger  centres  of  population.  The  Mahometan  calendar, 
a  lunar  one,  also  required  some  attention  in  order  that 
fasts  and  feasts  should  be  kept  at  the  proper  times.  More- 
over the  belief  in  the  possibility  of  predicting  the  future 
by  means  of  the  stars,  which  had  flourished  among  the 
Chaldaeans  (chapter  i.,  §  18),  but  which  remained  to  a  great 
extent  in  abeyance  among  the  Greeks,  now  revived  rapidly 
on  a  congenial  oriental  soil,  and  the  Caliphs  were  probably 
quite  as  much  interested  in  seeing  that  the  learned  men  of 

*  The  data  as  to  Indian  astronomy  are  so  uncertain,  and  the 
evidence  of  any  important  original  contributions  is  so  slight,  that  I 
have  not  thought  it  worth  while  to  enter  into  the  subject  in  any 
detail.  The  chief  Indian  treatises,  including  the  one  referred  to  in 
Ihe  text,  bear  strong  marks  of  having  been  based  on  Greek  writings. 


78  A  Short  History  of  Astronomy  [Cn.  in. 

their   courts  were  proficient   in  Astrology  as  in  astronomy 
proper. 

The  first  translation  of  the  Almagest  was  made  by  order 
of  Al  Mansur's  successor  Harun  al  Rasid  (A.D.  765  or  766 
-A.D.  809),  the  hero  of  the  Arabian  Nights.  It  seems, 
however,  to  have  been  found  difficult  to  translate  ;  fresh 
attempts  were  made  by  Honein  ben  Ishak  (?-873)  and 
by  his  son  Ishak  ben  Honein  (?-9io  or  911),  and  a  final 
version  by  Tabit  ben  Korra  (836-901)  appeared  towards 
the  end  of  the  gth  century.  Ishak  ben  Honein  translated 
also  a  number  of  other  astronomical  and  mathematical 
books,  so  that  by  the  end  of  the  gth  century,  after  which 
translations  almost  ceased,  most  of  the  more  important 
Greek  books  on  these  subjects,  as  well  as  many  minor 
treatises,  had  been  translated.  To  this  activity  we  owe 
our  knowledge  of  several  books  of  which  the  Greek  originals 
have  perished. 

57.  During   the   period   in  which  the   Caliphs  lived  at 
Damascus  an  observatory  was  erected  there,  and  another  on 
a  more  magnificent  scale  was  built  at  Bagdad  in  829  by  the 
Caliph  Al  Mamun.    The  instruments  used  were  superior  both 
in  size  and  in  workmanship  to  those  of  the  Greeks,  though 
substantially   of  the  same  type.      The  Arab  astronomers 
introduced   moreover    the    excellent   practice    of    making 
regular  and  as  far  as  possible  nearly  continuous  observa- 
tions of  the  chief  heavenly  bodies,  as  well  as  the  custom 
of  noting  the  positions  of  known  stars   at  the  beginning 
and  end  of  an  eclipse,  so  as  to  have  afterwards  an  exact 
record  of  the  times  of  their  occurrence.     So  much  import- 
ance was  attached  to  correct  observations  that  we  are  told 
that    those    of  special   interest   were   recorded   in   formal 
documents  signed  on  oath  by  a  mixed  body  of  astronomers 
and  lawyers. 

Al  Mamun  ordered  Ptolemy's  estimate  of  the  size  of  the 
earth  to  be  verified  by  his  astronomers.  Two  separate 
measurements  of  a  portion  of  a  meridian  were  made,  which, 
however,  agreed  so  closely  with  one  another  and  with 
the  erroneous  estimate  of  Ptolemy  that  they  can  hardly 
have  been  independent  and  careful  measurements,  but 
rather  rough  verifications  of  Ptolemy's  figures. 

58.  The  careful  observations  of  the  Arabs  soon  shewed 


$$  57— 6o]  The  Bagdad  School :  Albc.tcgnius  79 

the  defects  in  the  Greek  astronomical  tables,  and  new  tables 
were  from  time  to  time  issued,  based  on  much  the  same 
principles  as  those  in  the  Almagest ',  but  with  changes  in 
such  numerical  data  as  the  relative  sizes  of  the  various 
circles,  the  positions  of  the  apogees,  and  the  inclinations 
of  the  planes,  etc. 

To  Tabit  ben  Korra,  mentioned  above  as  the  translator  of 
the  Almagest,  belongs  the  doubtful  honour  of  the  ^discovery 
of  a  supposed  variation  in  the  amount  of  the  precession 
(chapter  n.,  §§  42,  50).  To  account  for  this  he  devised  a 
complicated  mechanism  which  produced  a  certain  alteration 
in  the  position  of  the  ecliptic,  thus  introducing  a  purely 
imaginary  complication,  known  as  the  trepidation,  which 
confused  and  obscured  most  of  the  astronomical  tables 
issued  during  the  next  five  or  six  centuries. 

59.  A  far  greater  astronomer  than  any  of  those  mentioned 
in  "the    preceding    articles   was    the   Arab    prince   called 
from  his  birthplace  Al  Battani,  and  better  known  by  the 
Latinised  name  Albategnius^  who  carried  on  observations 
from  878  to  918  and  died  in  929.     He  tested  many  of 
Ptolemy's    results    by    fresh    observations,    and    obtained 
more    accurate   values    of    the    obliquity   of    the    ecliptic  - 
(chapter  I.,    §   u)   and  of  precession.     He  wrote  also  a 
treatise   on   astronomy  which   contained   improved   tables 
of  the  sun  and  moon,  and  included  his  most  notable  dis-i 
covery — namely,    that   the   direction  of  the"  point    in   the) 
sun's   orbit   at   which   it    is   farthest   from   the    earth    (the: 
apogee),  or,  in  other  words,  the  direction  of  the  centre  of  j 
the   eccentric  representing   the   sun's  motion  (chapter  n.,' 
§  39),  was  not  the  same  as  that  given  in   the  Almagest  \ 
from  which   change,  too  great   to  be  attributed   to   mere 
errors   of  observation    or   calculation,    it    might   fairly    be 
inferred  that  the  apogee  was  slowly  moving,  a  result  which, 
however,  he  did  not  explicitly  state.     Albategnius  was  also 

a  good  mathematician,  and  the  author  of  some  notable 
improvements  in  methods  of  calculation.* 

60.  The  last  of  the  Bagdad  astronomers  was  Abul  Wafa 

*  He  introduced  into  trigonometry  the  use  of  sines,  and  made  also 
some  little  use  of  tangents,  without  apparently  realising  their  im- 
portance :  he  also  used  some  new  formulae  for  the  solution  of 
spherical  triangles. 


8o  A  Short  History  of  Astronomy  [Cn.  ill . 

(939  or  940-998),  the  author  of  a  voluminous  treatise  on 
astronomy  also  known  as  the  Almagest,  which  contained 
some  new  ideas  and  was  written  on  a  different  plan  from 
Ptolemy's  book,  of  which  it  has  sometimes  been  supposed 
to  be  a  translation.  In  discussing  the  theory  of  the  moon 
Abul  Wafa  found  that,  after  allowing  for  the  equation  of 
the  centre  and  for  the  evection,  there  remained  a  further 
irregularity  in  the  moon's  motion  which  was  imperceptible 
at  conjunction,  opposition,  and  quadrature,  but  appreciable 
at  the  intermediate  points.  It  is  possible  that  Abul  Waia 
here  detected  an  inequality  rediscovered  by  Tycho  JJrahe 
(chapter  v.,  §  in)  and  known  as  the  variation,  but  it 
is  equally  likely  that  he  was  merely  restating  Ptolemy's 
prosneusis  (chapter  n.,  §  48).*  In  either  case  Abul  Wafa's 
discovery  appears  to  have  been  entirely  ignored  by  his 
successors  and  to  have  borne  no  fruit.  He  also  carried 
further  some  of  the  mathematical  improvements  of  his 
predecessors. 

Another  nearly  contemporary  astronomer,  commonly 
known  as  Ibn  Yunos  (?-ioo8),  worked  at  Cairo  under 
the  patronage  of  the  Mahometan  rulers  of  Egypt.  He 
published  a  set  of  astronomical  and  mathematical  tables, 
the  Hakemite  Tables,  which  remained  the  standard  ones  for 
about  two  centuries,  and  he  embodied  in  the  same  book 
a  number  of  his  own  observations  as  well  as  an  extensive 
series  by  earlier  Arabian  astronomers. 

6 1.  About  this  time  astronomy,  in  common  with  other 
branches  of  knowledge,  had  made  some  progress  in  the 
Mahometan  dominions  in  Spain  and  the  opposite  coast 
of  Africa.  A  great  library  and  an  academy  were  founded 
at  Cordova  about  970,  and  centres  of  education  and  learning 
were  established  in  rapid  succession  at  Cordova,  Toledo, 
Seville,  and  Morocco. 

The  most  important  work  produced  by  the  astronomers 

of    these'  places    was    the  volume   of  astronomical    tables 

•  published  under   the  direction   of  Arzachel  in   1080,  and 

known  as  the    Toletan    Tables,  because   calculated  for  an 

observer   at  Toledo,  where  Arzachel  probably  lived.     To 

*  A  prolonged  but  indecisive  controversy  has  been  carried  on, 
chiefly  by  French  scholars,  with  regard  to  the  relations  of  Ptolemy, 
Abul  Wafa,  and  Tycho  in  this  matter. 


W  6x,  62]          77/£  Spanish  School:  Nassir  Eddin  t>i 

the  same  school  are  due  some  improvements  in  instru- 
ments and  in  methods  of  calculation,  and  several  writings 
were  published  in  criticism  of  Ptolemy,  without,  however, 
suggesting  any  improvements  on  his  ideas. 

Gradually,  however,  the  Spanish  Christians  began  to  drive 
back  their  Mahometan  neighbours.  Cordova  and  Seville 
were  captured  in  1236  and  1248  respectively,  and  with  their 
fall  Arab  astronomy  disappeared  from  history. 

62.  Before  we  pass  on  to  consider  the  progress  of 
astronomy  in  Europe,  two  more  astronomical  schools  of 
the  East  deserve  mention,  both  of  which  illustrate  an 
extraordinarily  rapid  growth  of. scientific  interests  among 
barbarous  peoples.  Hulagu  Khan,  a  grandson  of  the 
Mongol  conqueror  Qenghis  Khan,  captured  Bagdad  in  1258 
and  ended  the  rule  of  the  Caliphs  there.  Some  years 
before  this  he  had  received  into  favour,  partly  as  a  political 
adviser,  the  astronomer  Nassir  Eddin  (born  in  1201  at  Tus 
in  Khorassan),  and  subsequently  provided  funds  for  the 
establishment  of  a  magnificent  observatory  at  Meraga,  near 
the  north-west  frontier  of  modern  Persia.  Here  a  number 
of  astronomers  worked  under  the  general  superintendence 
of  Nassir  Eddin.  The  instruments  they  used  were  remark- 
able for  their  size  and  careful  construction,  and  were 
probably  better  than  any  used  in  Europe  in  the  time  of 
Copperniois,  being  surpassed  first  by  those  of  Tycho  Brahe 
(chapter  v.). 

Nassir  Eddin  and  his  assistants  translated  or  commented 
on  nearly  all  the  more  important  available  Greek  writings 
on  astronomy  and  allied  subjects,  including  Euclid's 
Elements,  several  books  by  Archimedes,  and  the  Almagest. 
Nassir  Eddin  also  wrote  an  abstract  of  astronomy,  marked 
by  some  little  originality,  and  a  treatise  on  geometry.  He 
does  not  appear  to  have  accepted  the  authority  of  Ptolemy 
without  question,  and  objected  in  particular  to  the  use 
of  the  equant  (chapter  n.,  §  51),  which  he  replaced  by 
a  new  combination  of  spheres.  Many  of  these  treatises 
had  for  a  long  time  a  great  reputation  in  the  East,  and 
became  in  their  turn  the  subject-matter  of  commentary. 

But  the  great  work  of  the  Meraga  astronomers,  which 
occupied  them  12  years,  was  the  issue  of  a  revised  set  of 
astronomical  tables,  based  on  the  Hakemite  Tables  of  Ibn 

6 


82  A  Short  History  of  Astronomy  [CH,  in. 

Yunos  (§  60),  and  called  in  honour  of  their  patron  the 
Ilkhanic  Tables.  They  contained  not  only  the  usual  tables 
for  computing  the  motions  of  the  planets,  etc.,  but  also  a 
star  catalogue,  based  to  some  extent  on  new  observations. 

An  important  result  of  the  observations  of  fixed  stars 
made  at  Meraga  was  that  the  precession  (chapter  n.,  §  42) 
was  fixed  at  51",  or  within  about  i''  of  its  true  value.  Nassir 
Eddin  also  discussed  the  supposed  trepidation  (§  58),  but 
seems  to  have  been  a  little  doubtful  of  its  reality.  He  died 
in  1273,  soon  after  his  patron,  and  with  him  the  Meraga 
School  came  to  an  end  as  rapidly  as  it  was  formed. 

63.  Nearly  two  centuries  later  Ulugh  Begh  (born  in  1394), 
a  grandson  of  the  savage  Tartar  Tamerlane,  developed  a 
great  personal  interest  in  astronomy,  and  built  about  1420  an 
observatory  at  Samarcand  (in  the  present  Russian  Turkestan), 
where   he   worked   with  assistants.      He   published   fresh 
tables  of  the  planets,   etc.,  but  his  most  important  work 
was  a  star  catalogue,  embracing  nearly  the  same  stars  as 
that  of  Ptolemy,  but  observed  afresh.     This  was  probably 
the   first  substantially  independent  catalogue   made   since 
Hipparchus.      The   places   of  the   stars   were   given  wiih 
unusual    precision,    the   minutes    as   well   as   the   degrees 
of  celestial  longitude   and   latitude   being  recorded;    and 
although   a   comparison   with    modern   observation   shews 
that   there   were   usually  errors    of  several    minutes,  it   is 
probable  that  the  instruments  used  were  extremely  good. 
Ulugh  Begh  was  murdered  by  his  son  in  1449,  ar]d  with 
hun  Tartar  astronomy  ceased. 

64.  No  great  original  idea  can  be  attributed  to  any  of  the 
Arab  and  other  astronomers  whose  work  we  have  sketched. 

/They  had,  however,  a  remarkable  aptitude  for  absorbing 
/  foreign  ideas,   and   carrying  them  slightly  further.     They 
^  were  patient  and  accurate  observers,  and  skilful  calculators. 
We  owe  to  them  a  long  series  of  observations,  and  the 
invention  or   introduction   of  several   important   improve- 
ments   in    mathematical    methods.*      Among    the    most 
important  of  their  services  to  mathematics,  and  hence  to 
astronomy,  must  be  counted  the  introduction,  from  India, 

*  For  example,  the  practice  of  treating  the  trigonometrical  functions 
as  algebraic  quantities  to  be  manipulated  by  formulae,  not  merely 
as  geometrical  lines. 


$§  63—65]      Ulugh  Begh  :  Estimate  of  Arab  Astronomy       83 

of  our  present  system  of  writing  numbers,  by  which  the 
value  of  a  numeral  is  altered  by  its  position,  and  fresh 
symbols  are  not  wanted,  as  in  the  clumsy  Greek  and 
Roman  systems,  for  higher  numbers.  An  immense  sim- 
plification was  thereby  introduced  into  arithmetical  work.*' 
More  important  than  the  actual  original  contributions  of 
the  Arabs  to  astronomy  was  the  service  that  they  perform jJ 
in  keeping  alive  interest  in  the  science  and  preserving  the 
discoveries  of  their  Greek  predecessors. 

Some  curious  relics  of  the  time  when  the  Arabs  were 
the  great  masters  in  astronomy  have  been  preserved  in 
astronomical  language.  Thus  we  have  derived  from  them, 
usually  in  very  corrupt  forms,  the  current  names  of  many  % 
individual  stars,  e.g.  Aldebaran,  Altair,  Betelgeux,  Kigel, 
Vega  (the  constellations  being  mostly  known  by  Latin 
translations  of  the  Greek  names),  and  some  common 
astronomical  terms  such  as  zenith  and  nadir  (the  invisible 
point  on  the  celestial  sphere  opposite  the  zenith) ;  while 
at  least  one  such  word,  almanack,  has  passed  into  common 
language. 

65.  In  Europe  the  period  of  confusion  following  the  break- 
up of  the  Roman  empire  and  preceding  the  definite  formation 
of  feudal  Europe  is  almost  a  blank  as  regards  astronomy, 
or  indeed  any  other  natural  science.  The  best  intellects 
that  were  not  absorbed  in  practical  life  were  occupied 
with  theology.  A  few  men,  such  as  the  Venerable  Bede 
(672-735),  living  for  the  most  part  in  secluded  monasteries, 
were  noted  for  their  learning,  which  included  in  general 
some  portions  of  mathematics  and  astronomy ;  none  were 
noted  for  their  additions  to  scientific  knowledge.  Some 
advance  was  made  by  Charlemagne  (742-814),  who,  in 
addition  to  introducing  something  like  order  into  his 
extensive  dominions,  made  energetic  attempts  to  develop 
education  and  learning.  In  782  he  summoned  to  his  court 
our  learned  countryman  Alcnin  (735-804)  to  give  instruction 
in  astronomy,  arithmetic,  and  rhetoric,  as  well  as  in  other 
subjects,  and  invited  other  scholars  to  join  him,  forming 
thus  a  kind  of  Academy  of  which  Alcuin  was  the  head. 

*  Any  one  who  has  not  realised   this  may  do  so  by  performing 
with  Roman  numerals  the  simple  operation  of  multiplying  by  itself 
number  such  as  MDCCCXCVUI. 


84  A  Short  History  of  Astronomy  [CH.  ill. 

Charlemagne  not  only  founded  a  higher  school  at  his 
own  court,  but  was  also  successful  in  urging  the  ecclesi- 
astical authorities  in  all  parts  of  his  dominions  to  do 
the  same.  In  these  schools  were  taught  the  seven  liberal 
arts,  divided  into  the  so-called  trivium  (grammar,  rhetoric, 
and  dialectic)  and  quadrivium,  which  included  astronomy 
in  addition  to  arithmetic,  geometry,  and  music. 

66.  In  the  loth  century  the  fame  of  the  Arab  learning 
began  slowly  to  spread  through  Spain  into  other  parts  of 
Europe,  and  the  immense  learning  of  Gerbert,  the  most 
famous  scholar  of  the  century,  who  occupied  the  papal 
chair  as  Sylvester  II.  from  999  to  1003,  was  attributed  in 
large  part  to  the  time  which  he  spent  in  Spain,  either  in 
or  near  the  Moorish  dominions.  He  was  an  ardent  student, 
indefatigable  in  collecting  and  reading  rare  books,  and 
was  especially  interested  in  mathematics  and  astronomy. 
His  skill  in  making  astrolabes  (chapter  IL,  §  49)  and  other 
instruments  was  such  that  he  was  popularly  supposed  to 
have  acquired  his  powers  by  selling  his  soul  to  the  Evil 
One.  Other  scholars  shewed  a  similar  interest  in  Arabic 
learning,  but  it  was  not  till  the  lapse  of  another  century 
that  the  Mahometan  influence  became  important. 

At  the  beginning  of  the  i2th  century  began  a  series  of 
translations  from  Arabic  into  Latin  of  scientific  and 
philosophic  treatises,  partly  original  works  of  the  Arabs, 
partly  Arabic  translations  of  the  Greek  books.  One  of  the 
most  active  of  the  translators  was  Plato  of  Tivoli,  who 
studied  Arabic  in  Spain  about  1116,  and  translated  Alba- 
tegnius's  Astronomy  (§  59),  as  well  as  other  astronomical 
books.  At  about  the  same  time  Euclid's  Elements,  among 
other  books,  was  translated  by  Athelard  of  Bath.  Gherardo 
of  Cremona  (1114-1187)  was  even  more  industrious,  and 
is  said  to  have  made  translations  of  about  70  scientific 
treatises,  including  the  Almagest,  and  the  Toletan  Tables 
of  Arzachel  (§  61).  The  beginning  of  the  i3th  century  was 
marked  by  the  foundation  of  several  Universities,  and  at 
that  of  Naples  (founded  in  1224)  the  Emperor  Frederick  II. , 
who  had  come  into  contact  with  the  Mahometan  learning 
in  Sicily,  gathered  together  a  number  of  scholars  whom  he 
directed  to  make  a  fresh  series  of  translations  from  the 
Arabic. 


§*  66,  67]        The  Revival  of  Astronomy  in  the   West  85 

Aristotle's  writings  on  logic  had  been  preserved  in 
Latin  translations  from  classical  times,  and  were  already 
much  esteemed  by  the  scholars  of  the  nth  and  i2th 
centuries.  His  other  writings  were  first  met  with  in  Arabic 
versions,  and  were  translated  into  Latin  during  the  end 
of  the  1 2th  and  during  the  i3th  centuries;  in  one  or  two 
cases  translations  were  also  made  from  the  original  Greek. 
The  influence  of  Aristotle  over  medieval  thought,  already 
considerable,  soon  became  almost  supreme,  and  his  works 
were  by  many  scholars  regarded  with  a  reverence  equal  to 
or  greater  than  that  felt  for  the  Christian  Fathers. 

Western  knowledge  of  Arab  astronomy  was  very  much 
increased  by  the  activity  of  Alfonso  X.  of  Leon  and  Castile 
(1223-1284),  who  collected  at  Toledo,  a  recent  conquest 
from  the  Arabs,  a  body  of  scholars,  Jews  and  Christians, 
who  calculated  under  his  general  superintendence  a  set  of 
new  astronomical  tables  to  supersede  the  Toletan  Tables. 
These  Alfonsine  Tables  were  published  in  1252,  on  the 
day  of  Alfonso's  accession,  and  spread  rapidly  through 
Europe.  They  embodied  no  new  ideas,  but  several 
numerical  data,  notably  the  length  of  the  year,  were 
given  with  greater  accuracy  than  before.  To  Alfonso  is 
due  also  the  publication  of  the  Libros  del  Saber,  a  volu- 
minous encyclopaedia  of  the  astronomical  knowledge  of 
the  time,  which,  though  compiled  largely  from  Arab  sources, 
was  not,  as  has  sometimes  been  thought,  a  mere  collection 
of  translations.  One  of  the  curiosities  in  this  book  is  a 
diagram  representing  Mercury's  orbit  as  an  ellipse,  the 
earth  being  in  the  centre  (cf.  chapter  vii.,  §  140),  this 
being  probably  the  first  trace  of  the  idea  of  representing 
the  celestial  motions  by  means  of  curves  other  than  circles. 

67.  To  the  1 3th  century  belong  also  several  of  the  great 
scholars,  such  as  Albertus  Magnus,  Roger  Bacon,  and 
Cecco  (TAscoli  (from  whom  Dante  learnt),  who  -took  all 
knowledge  for  their  province.  Roger  Bacon,  who  was  born 
in  Somersetshire  about  1214  and  died  about  1294,  wrote 
three  principal  books,  called  respectively  the  Opus  Majus, 
Opus  Minus,  and  Opus  Tertium,  which  contained  not  only 
treatises  on  most  existing  branches  of  knowledge,  but  also 
some  extremely  interesting  discussions  of  their  relative 
importance  and  of  the  right  method  for  the  advancement 


86  A  SJiort  His/orv  of  Astronomy  [Cn.  in. 

. 

of  learning.  He  inveighs  warmly  against  excessive  adher- 
ence to  authority,  especially  to  that  of  Aristotle,  whose 
books  he  wishes  burnt,  and  speaks  strongly  of  the  import- 
ance of  experiment  and  of  mathematical  reasoning  in 
scientific  inquiries.  He  evidently  had  a  good  knowledge 
of  optics  and  has  been  supposed  to  have  been  acquainted 
with  the  telescope,  a  supposition  which  we  can  hardly 
regard  as  confirmed  by  his  story  that  the  invention  was 
known  to  Caesar,  who  when  about  to  invade  Britain  sur- 
veyed the  new  country  from  the  opposite  shores  of  Gaul 
with  a  telescope  ! 

Another  famous  book  of  this  period  was  written  by  the 
Yorkshireman  John  Halifax  or  Holywood,  better  known 
by  his  Latinised  name  Sacrobosco,  who  was  for  some  time 
a  well-known  teacher  of  mathematics  at  Paris,  where  he 
died  about  1256.  His  Sphaera  Mundiws  an  elementary 
treatise  on  the  easier  parts  of  current  astronomy,  dealing 
in  fact  with  little  but  the  more  obvious  results  of  the 
daily  motion  of  the  celestial  sphere.  It  enjoyed  immense 
popularity  for  three  or  four  centuries,  and  was  frequently 
re-edited,  translated,  and  commented  on  :  it  was  one  of 
the  very  first  astronomical  books  ever  printed  ;  25  editions 
appeared  between  1472  and  the  end  of  the  century,  and 
40  more  by  the  middle  of  the  lyth  century. 

68.  The  European  writers  of  the  Middle  Ages  whom  we 
have  hitherto  mentioned,  with  the  exception  of  Alfonso  and 
his  assistants,  had  contented  themselves  with  collecting  and 
rearranging  such  portions  of  the  astronomical  knowledge 
of  the  Greeks  and  Arabs  as  they  could  master ;  there  were 
no  serious  attempts  at  making  progress,  and  no  observations 
of  importance  were  made.  A  new  school,  however,  grew 
up  in  Germany  during  the  i5th  century  which  succeeded 
in  making  some  additions  to  knowledge,  not  in  themselves 
of  first-rate  importance,  but  significant  of  the  greater  inde- 
pendence that  was  beginning  to  inspire  scientific  work. 
George  Purbach,  born  in  1423,  became  in  1450  professor 
of  astronomy  and  mathematics  at  the  University  of  Vienna, 
which  had  soon  after  its  foundation  (1365)  become  a 
centre  for  these  subjects.  He  there  began  an  Epitome 
of  Astronomy  based  on  the  Almagest ',  and  also  a  Latin 
version  of  Ptolemy's  planetary  theory,  intended  partly 


§  68]  SacroboscO)  Purbach,  Regiomontanus  87 

as  a  supplement  to  Sacrobosco's  textbook,  from  which 
this  part  of  the  subject  had  been  omitted,  but  in  part 
also  as  a  treatise  of  a  higher  order ;  but  he  was  hindered 
in  both  undertakings  by  the  badness  of  the  only  available 
versions  of  the  Almagest — Latin  translations  which  had 
been  made  not  directly  from  the  Greek,  but  through 
the  medium  at  any  rate  of  Arabic  and  very  possibly  of 
Syriac  as  well  (cf.  §  56),  and  which  consequently  swarmed 
with  mistakes.  He  was  assisted  in  this  work  by  his  more 
famous  pupil  John  Miiller  of  Konigsberg  (in  Franconia), 
hence  known  as  Regiomontanus,  who  was  attracted  to 
Vienna  at  the  age  of  16  (1452)  by  Purbach's  reputation. 
The  two  astronomers  made  some  observations,  and  were 
strengthened  in  their  conviction  of  the  necessity  of  astro- 
nomical reforms  by  the  serious  inaccuracies  which  they 
discovered  in  the  Alfonsine  Tables,  now  two  centuries  old ; 
an  eclipse  of  the  moon,  for  example,  occurring  an  hour  late 
and  Mars  being  seen  2°  from  its  calculated  place.  Purbach 
and  Regiomontanus  were  invited  to  Rome  by  one  of  the 
Cardinals,  largely  with  a  view  to  studying  a  copy  of  the 
Almagest  contained  among  the  Greek  manuscripts  which 
since  the  fall  of  Constantinople  (1453)  had  come  into  Italy 
in  considerable  numbers,  and  they  were  on  the  point  of 
starting  when  the  elder  man  suddenly  died  (1461). 

Regiomontanus,  who  decided  on  going  notwithstanding 
Purbach's  death,  was  altogether  seven  years  in  Italy  ;  he 
there  acquired  a  good  knowledge  of  Greek,  which  he  had 
already  begun  to  study  in  Vienna,  and  was  thus  able  to  read 
the  Almagest  and  other  treatises  in  the  original ;  he  completed 
Purbach's  Epitome  of  Astronomy,  made  some  observations, 
lectured,  wrote  a  mathematical  treatise  *  of  considerable 
merit,  and  finally  returned  to  Vienna  in  1468  with  originals 
or  copies  of  several  important  Greek  manuscripts.  He 
was  for  a  short  time  professor  there,  but  then  accepted  an 
invitation  from  the  King  of  Hungary  to  arrange  a  valuable 
collection  of  Greek  manuscripts.  The  king,  however,  soon 

*  On  trigonometry.  He  reintroduced  the  stne,  which  had  been 
forgotten  ;  and  made  some  use  of  the  tangent,  but  like  AJbategnius 
(§  59 n-)  did  not  realise  its  importance,  and  thus  remained  behind 
Ibn  Yunos  and  Abul  Wafa.  An  important  contribution  to  mathe- 
matics was  a  table  of  sines  calculated  for  every  minute  from  o°  to  90°. 


88  A  Short  History  of  Astronomy  [Cn.  in. 

turned  his  attention  from  Greek  to  fighting,  and  Regiomon- 
tanus  moved  once  more,  settling  this  time  in  Niirnberg,  then 
one  of  the  most  flourishing  cities  in  Germany,  a  special 
attraction  of  which  was  that  one  of  the  early  printing 
presses  was  established  there.  The  Niirnberg  citizens 
received  Regiomontanus  with  great  honour,  and  one  rich 
man  in  particular,  Bernard  Walther  (1430-1504),  not  only 
supplied  him  with  funds,  but,  though  an  older  man,  became 
his  pupil  and  worked  with  him.  The  skilled  artisans  of 
Niirnberg  were  employed  in  constructing  astronomical 
instruments  of  an  accuracy  hitherto  unknown  in  Europe, 
though  probably  still  inferior  to  those  of  Nassir  Eddin  and 
Ulugh  Begh  (§§  62,  63).  A  number  of  observations  were 
made,  among  the  most  interesting  being  those  of  the  comet 
of  1472,  the  first  comet  which  appears  to  have  been 
regarded  as  a  subject  for  scientific  study  rather  than  for 
superstitious  terror.  Regiomontanus  recognised  at  once  the 
importance  for  his  work  of  the  new  invention  of  printing, 
and,  finding  probably  that  the  existing  presses  were  unable 
to  meet  the  special  requirements  of  astronomy,  started  a 
printing  press  of  his  own.  Here  he  brought  out  in  1472 
or  1473  an  edition  of  Purbach's  book  on  planetary  theory, 
which  soon  became  popular  and  was  frequently  reprinted. 
This  book  indicates  clearly  the  discrepancy  already  being 
felt  between  the  views  of  Aristotle  and  those  of  Ptolemy. 
Aristotle's  original  view  was  that  sun,  moon,  the  five 
planets,  and  the  fixed  stars  were  attached  respectively  to 
eight  spheres,  one  inside  the  other ;  and  that  the  outer 
one,  which  contained  the  fixed  stars,  by  its  revolution  was 
the  primary  cause  of  the  apparent  daily  motion  of  all  the 
celestial  bodies.  The  discovery  of  precession  required  on 
the  part  of  those  who  carried  on  the  Aristotelian  tradition 
the  addition  of  another  sphere.  According  to  this  scheme, 
which  was  probably  due  to  some  of  the  translators  or 
commentators  at  Bagdad  (§  56),  the  fixed  stars  were  on 
a  sphere,  often  called  the  firmament,  and  outside  this  was 
a  ninth  sphere,  known  as  the  primum  mobile,  which  moved 
all  the  others ;  another  sphere  was  added  by  Tabit  ben 
Korra  to  account  for  trepidation  (§  58),  and  accepted  by 
Alfonso  and  his  school ;  an  eleventh  sphere  was  added 
towards  the  end  of  the  Middle  Ages  to  account  for  the 


68] 


The  Celestial  Spheres 


89 


supposed  changes  in  the  obliquity  of  the  ecliptic.  A  few 
writers  invented  a  larger  number.  Outside  these  spheres 
mediaeval  thought  usually  placed  the  Empyrean  or  Heaven. 
The  accompanying  diagram  illustrates  the  w hole  arrange- 
ment. 


FIG.  36. — The  celestial  spheres.     From  Apian's  Cosmograpfnu. 

These  spheres,  which  were  almost  entirely  fanciful  and 
in  no  serious  way  even  professed  to  account  for  the  details 
of  the  celestial  motions,  are  of  course  quite  different  from 
the  circles  known  as  deferents  and  epicycles,  which  Hippar- 
chus  and  Ptolemy  used.  These  were  mere  geometrical 


90  A  Short  History  of  Astronomy  [Cn.  ill 

abstractions,  which  enabled  the  planetary  motions  to  be 
represented  with  tolerable  accuracy.  Each  planet  moved 
freely  in  space,  its  motion  being  represented  or  described 
(not  controlled}  by  a  particular  geometrical  arrangement 
of  circles.  Purbach  suggested  a  compromise  by  hollowing 
out  Aristotle's  crystal  spheres  till  there  was  room  for 
Ptolemy's  epicycles  inside  ! 

From  the  new  Niirnberg  press  were  issued  also  a  suc- 
cession of  almanacks  which,  like  those  of  to-day,  gave  the 
public  useful  information  about  moveable  feasts,  the  phases 
of  the  moon,  eclipses,  etc. ;  and,  in  addition,  a  volume  of 
less  popular  Ephemerides^  with  astronomical  information 
of  a  fuller  and  more  exact  character  for  a  period  of  about 
30  years.  This  contained,  among  other  things,  astronomical 
data  for  finding  latitude  and  longitude  at  sea,  for  which 
Regiomontanus  had  invented  a  new  method.* 

The  superiority  of  these  tables  over  any  others  available 
was  such  that  they  were  used  on  several  of  the  great  voyages 
of  discovery  of  this  period,  probably  by  Columbus  himself 
on  his  first  voyage  to  America. 

•  In  1475  Regiomontanus  was  invited  to  Rome  by  the 
Pope  to  assist  in  a  reform  of  the  calendar,  but  died  there 
the  next  year  at  the  early  age  of  forty. 

Walther  carried  on  his  friend's  work  and  took  a  number 
of  good  observations;  he  was  the  first  to  make  any 
successful  attempt  to  allow  for  the  atmospheric  refraction 
of  which  Ptolemy  had  probably  had  some  knowledge  (chap- 
ter ii.,  §  46) ;  to  him  is  due  also  the  practice  of  obtaining 
the  position  of  the  sun  by  comparison  with  Venus  instead  of 
with  the  moon  (chapter  n.,  §  39),  the  much  slower  motion 
of  the  planet  rendering  greater  accuracy  possible. 

After  Walther's  death  other  observers  of  less  merit  carried 
on  the  work,  and  a  Niirnberg  astronomical  school  of  some 
kind  lasted  into  the  iyth  century. 

69.  A  few  minor  discoveries  in  astronomy  belong  to  this 
or  to  a  slightly  later  period  and  may  conveniently  be  dealt 
with  here. 

""  Lionardo  da  Vinci*  (1452-1519),  who  was  not  only  a 
great  painter  and  sculptor,  but  also  an  anatomist,  engineer, 
mechanician,  physicist,  and  mathematician,  was  the  first 

*  That  of  "  lunar  distances."  ^/^ 

yy;  yC-If^*. 


$69]  Regiomontanus  and  Others  91 

to  explain  correctly  the  dim  illumination  seen  over  the 
rest  of  the  surface  of  the  moon  when  the  bright  part  is 
only  a  thin  crescent.  He  pointed  out  that  when  the 
moon  was  nearly  new  the  half  of  the  earth  which  was 
then  illuminated  by  the  sun  was  turned  nearly  directly 
towards  the  moon,  and  that  the  moon  was  in  consequence 
illuminated  slightly  by  this  earthshine,  just  as  we  are  by 
moonshine.  The  explanation  is  interesting  in  itself,  and 
was  also  of  some  value  as  shewing  an  analogy  between 
the  earth  and  moon  which  tended  to  break  down  the 
supposed  barrier  between  terrestrial  and  celestial  bodies 
(chapter  vi.,  §  1 19). 

Jerome  Fracas  for  (1483-1543)  and  Peter  Apian  (1495- 
1552),  two  voluminous  writers  on  astronomy,  made  obser- 
vations of  comets  of  some  interest,  both  noticing  that 
a  comet's  tail  continually  points  away  from  the  sun,  as 
the  comet  changes  its  position,  a  fact  which  has  been 
used  in  modern  times  to  throw  some  light  on  the  structure 
of  comets  (chapter  xni.,  §  304). 

Peter  Nonius  (1492-1577)  deserves  mention  on  account 
of  the  knowledge  of  twilight  which  he  possessed ;  several 
problems  as  to  the  duration  of  twilight,  its  variation  in 
different  latitudes,  etc.,  were  correctly  solved  by  him  ;  but 
otherwise  his  numerous  books  are  of  no  great  interest.* 

A  new  determination  of  the  size  of  the  earth,  the  first 
since  the  time  of  the  Caliph  Al  Mamun  (§  57),  was  made 
about  1528  by  the  French  doctor  John  Fernel  (1497-1558), 
who  arrived  at  a  result  the  error  in  which  (less  than  i  per 
cent.)  was  far  less  than  could  reasonably  have  been  ex- 
pected from  the  rough  methods  employed. 

The  life  of  Regiomontanus  overlapped  that  of  Copper- 
nicus  by  three  years  ;  the  four  writers  last  named  were 
nearly  his  contemporaries ;  and  we  may  therefore  be  said  to 
have  come  to  the  end  of  the  comparatively  stationary  period 
dealt  with  in  this  chapter. 

*  He  did  not  invent  the  measuring  instrument  called  the  vernier, 
often  attributed  to  him,  but  something  quite  different  and  of  very 
inferior  value. 


CHAPTER   IV. 

COPPERNICUS. 

"But  in  this  our  age,  one  rara  witte  (seeing  the  continuall  errors 
that  from  time  to  time  more  and  more  continually  have  been  dis- 
covered, besides  the  infinite  absurdities  in  their  Theoricks,  which 
they  have  been  forced  to  admit  that  would  not  confesse  any  Mobilitie 
in  the  ball  of  the  Earth)  hath  by  long  studye,  paynfull  practise, 
and  rare  invention  delivered  a  new  Theorick  or  Model  of  the  world, 
shewing  that  the  Earth  resteth  not  in  the  Center  of  the  whole  world 
or  globe  of  elements,  which  encircled  and  enclosed  in  the  Moone's 
orbit,  and  together  with  the  whole  globe  of  mortality  is  carried 
yearly  round  about  the  Sunne,  which  like  a  king  in  the  middest  of 
.all,  rayneth  and  give.th  laws  of  motion  to  all  the  rest,  sphaerically 
dispersing  his  glorious  beames  of  light  through  all  this  sacred 
coelestiall  Temple." 

THOMAS  DIGGES,  1 590. 

70.  THE  growing  interest  in  astronomy  shewn  by  the 
work  of  such  men  as  Regiomontanus  was  one  of  the  early 
results  in  the  region  of  science  of  the  great  movement  of 
thought  to  different  aspects  of  which  are  given  the  names 
of  Revival  of  Learning,  Renaissance,  and  Reformation. 
The  movement  may  be  regarded  primarily  as  a  general 
quickening  of  intelligence  and  of  interest  in  matters  of 
thought  and  knowledge.  The  invention  of  printing  early 
in  the  i5th  century,  the  stimulus  to  the  study  of  the  Greek 
authors,  due  in  part  to  the  scholars  who  were  driven  west- 
wards after  the  capture  of  Constantinople  by  the  Turks 
(1453),  and.  the  discovery  of  America  by  Columbus  in 
1492,  all  helped  on  a  movement  the  beginning  of  which 
has  to  be  looked  for  much  earlier. 

Every  stimulus  to  the  intelligence  naturally  brings  with  it 
a  tendency  towards  inquiry  into  opinions  received  through 
tradition  and  based  on  some  great  authority.  The  effective 

92 


CH.  IV.,  $$  70, 7i]         The  Revival  of  Learning  93 

discovery  and  the  study  of  Greek  philosophers  other 
than  Aristotle  naturally  did  much  to  shake  the  supreme 
authority  of  that  great  philosopher,  just  as  the  Reformers 
shook  the  authority  of  the  Church  by  pointing  out  what 
they  considered  to  be  inconsistencies  between  its  doctrines 
and  those  of  the  Bible.  At  first  there  was  little  avowed 
opposition  to  the  principle  that  truth  was  to  be  derived 
from  some  authority,  rather  than  to  be  sought  independ- 
ently by  the  light  of  reason ;  the  new  scholars  replaced 
the  authority  of  Aristotle  by  that  of  Plato  or  of  Greek  and 
Roman  antiquity  in  general,  and  the  religious  Reformers 
replaced  the  Church  by  the  Bible.  Naturally,  however, 
the  conflict  between  authorities  produced  in  some  minds 
scepticism  as  to  the  principle  of  authority  itself;  when 
freedom  of  judgment  had  to  be  exercised  to  the  extent 
of  deciding  between  authorities,  it  was  but  a  step  further 
— a  step,  it  is  true,  that  comparatively  few  took — to  use 
the  individual  judgment  on  the  matter  at  issue  itself. 

In  astronomy  the  conflict  between  authorities  had  already 
arisen,  partly  in  connection  with  certain  divergencies  be- 
tween Ptolemy  and  Aristotle,  partly  in  connection  with 
the  various  astronomical  tables  which,  though  on  sub- 
stantially the  same  lines,  differed  in  minor  points.  The 
time  was  therefore  ripe  for  some  fundamental  criticism  of 
the  traditional  astronomy,  and  for  its  reconstruction  on  a 
new  basis. 

Such  a  fundamental  change  was  planned  and  worked 
out  by  the  great  astronomer  whose  work  has  next  to  be 
considered. 

71.  Nicholas  Coppernic  or  Coppernicus^  was  born  on 
February  iQth,  1473,  m  a  house  still  pointed  out  in  the  Httle 
trading  town  of  Thorn  on  the  Vistula.  Thorn  now  lies 
just  within  the  eastern  frontier  of  the  present  kingdom  of 
Prussia ;  in  the  time  of  Coppernicus  it  lay  in  a  region  over 
which  the  King  of  Poland  had  some  sort  of  suzerainty,  the 

*  The  name  is  spelled  in  a  large  number  of  different  ways  both  by 
Coppernicus  and  by  his  contemporaries.  He  himself  usually  wrote 
his  name  Coppernic,  and  in  learned  productions  commonly  used  the 
Latin  form  Coppernicus.  The  spelling  Copernicus  is  so  much  less 
commonly  used  by  him  that  I  have  thought  it  better  to  discard  it, 
even  at  the  risk  of  appearing  pedantic. 


94  ^  Short  History  of  Astronomy  [CH.  IV. 

precise  nature  of  which  was  a  continual  subject  of  quarrel 
between  him,  the  citizens,  and  the  order  of  Teutonic  knights, 
who  claimed  a  good  deal  of  the  neighbouring  country. 
The  astronomer's  father  (whose  name  was  most  commonly 
written  Koppernigk)  was  a  merchant  w.io  came  to  Thorn 
from  Cracow,  then  the  capital  of  Poland,  in  1462.  Whether 
Coppernicus  should  be  counted  as  a  Pole  or  as  a  German 
is  an  intricate  question,  over  which  his  biographers  have 
fought  at  great  length  and  with  some  acrimony,  but  which 
is  not  worth  further  discussion  here. 

Nicholas,  after  the  death  of  his  father  in  1483,  was  under 
the  care  of  his  uncle,  Lucas  Watzelrode,  afterwards  bishop 
of  the  neighbouring  diocese  of  Ermland,  and  was  destined 
by  him  from  a  very  early  date  for  an  ecclesiastical  career. 
He  attended  the  school  at  Thorn,  and  at  the  age  of  17 
entered  the  University  of  Cracow.  Here  he  seems  to  have 
first  acquired  (or  shewn)  a  decided  taste  for  astronomy 
and  mathematics,  subjects  in  which  he  probably  received 
help  from  Albert  Brudzewski,  who  had  a  great  reputation 
as  a  learned  and  stimulating  teacher ;  the  lecture  lists  of 
the  University  show  that  the  comparatively  modern  treatises 
of  Purbach  and  Regiomontanus  (chapter  in.,  §  68)  were 
the  standard  textbooks  used.  Coppernicus  had  no  intention 
of  graduating  at  Cracow,  and  probably  left  after  three 
years  (1494).  During  the  next  year  or  two  he  lived 
partly  at  home,  partly  at  his  uncle's  palace  at  Heilsberg, 
and  spent  some  of  the  time  in  an  unsuccessful  candidature 
for  a  canonry  at  Frauenburg,  the  cathedral  city  of  his 
uncle's  diocese. 

The  next  nine  or  ten  years  of  his  life  (from  1496  to 
1505  or  1506)  were  devoted  to  studying  in  Italy,  his  stay 
there  being  broken  only  by  a  short  visit  to  Frauenburg  in 
1501.  He  worked  chiefly  at  Bologna  and  Padua,  but 
graduated  at  Ferrara,  and  also  spent  some  time  at  Rome, 
where  his  astronomical  knowledge  evidently  made  a  favour- 
able impression.  Although  he  was  supposed  to  be  in 
Italy  primarily  with  a  view  to  studying  law  and  medicine, 
it  is  evident  that  much  of  his  best  work  was  being  put 
into  mathematics  and  astronomy,  while  he  also  paid  a  good 
deal  of  attention  to  Greek. 

During  his  absence  he  was  appointed  (about   1497)  to 


COPPERN1CUS. 


\Tofacep.  94. 


$  72j  Life  of  Coppernicus  95 

a  canonry  at  Frauenburg,  and  at  some  uncertain  date 
he  also  received  a  sinecure  ecclesiastical  appointment  at 
Breslau. 

72.  On  returning  to  Frauenburg  from  Italy  Coppernicus 
almost  immediately  obtained  fresh  leave  of  absence,  and 
joined  his  uncle  at  Heilsberg,  ostensibly  as  his  medical 
adviser  and  really  as  his  companion. 

It  was  probably  during  the  quiet  years  spent  at  Heilsberg 
that  he  first  put  into  shape  his  new  ideas  about  astronomy, 
nnd  wrote  the  first  draft  of  his  book.  He  kept  the 
manuscript  by  him,  revising  and  rewriting  from  time  to 
time,  partly  from  a  desire  to  make  his  work  as  perfect  as 
possible,  partly  from  complete  indifference  to  reputation, 
coupled  with  dislike  of  the  controversy  to  which  the 
publication  of  his  book  would  almost  certainly  give  rise. 
In  1509  he  published  at  Cracow  his  first  book,  a  Latin 
translation  of  a  set  of  Greek  letters  by  Theophylactus, 
interesting  as  being  probably  the  first  translation  from  the 
Greek  ever  published  in  Poland  or  the  adjacent  districts. 
In  1512,  on  the  death  of  his  uncle,  he  finally  settled  in 
Frauenburg,  in  a  set  of  rooms  which  he  occupied,  with  short 
intervals,  for  the  next  31  years.  Once  fairly  in  residence, 
he  took  his  share  in  conducting  the  business  of  the 
Chapter:  he  acted,  for  example,  more  than  once  as  their 
representative  in  various  quarrels  with  the  King  of  Poland 
and  the  Teutonic  knights;  in  1523  he  was  general 
administrator  of  the  diocese  for  a  few  months  after  the 
death  of  the  bishop  ;  and  for  two  periods,  amounting  alto- 
gether to  six  years  (1516-1519  and  1520-1521),  he  lived  at 
the  castle  of  Allenstein,  administering  some  of  the  outlying 
property  of  the  Chapter.  In  1521  he  was  commissioned  to 
draw  up  a  statement  of  the  grievances  of  the  Chapter 
against  the  Teutonic  knights  for  presentation  to  the 
Prussian  Estates,  and  in  the  following  year  wrote  a  memo- 
randum on  the  debased  and  confused  state  of  the  coinage 
in  the  district,  a  paper  which  was  also  laid  before  the 
Estates,  and  was  afterwards  rewritten  in  Latin  at  the  special 
request  of  the  bishop.  He  also  gave  a  certain  amount 
of  medical  advice  to  his  friends  as  well  as  to  the  poor  of 
Frauenburg,  though  he  never  practised  regularly  as  a 
physician  ;  but  notwithstanding  these  various  occupations 


g6  A  Short  History  of  Astronomy  [CH.  iv. 

it  is  probable  that  a  very  large  part  of  his  time  during  the 
last  30  years  of  his  life  was  devoted  to  astronomy. 

73.  We  are  so  accustomed  to  associate  the  revival  of 
astronomy,  as  of  other  branches  of  natural  science,  with 
increased  care  in  the  collection  of  observed  facts,  and  to 
think  of  Coppernicus  as  the  chief  agent  in  the  revival,  that 
it  is  worth  while  here  to  emphasise  the  fact  that  he  was  in 
no  sense  a  great  observer.  His  instruments,  which  were 
mostly  of  his  own  construction,  were  far  inferior  to  those 
of  Nassir  Eddin  and  of  Ulugh  Begh  (chapter  in.,  §§  62,  63), 
and  not  even  as  good  as  those  which  he  could  have  pro- 
cured if  he  had  wished  from  the  workshops  of  Niirnberg ; 
his  observations  were  not  at  all  numerous  (only  27,  which 
occur  in  his  book,  and  a  dozen  or  two  besides  being  known), 
and  he  appears  to  have  made  no  serious  attempt  to  secure 
great  accuracy.  His  determination  of  the  position  of  one 
star,  which  was  extensively  used  by  him  as  a  standard  of 
reference  and  was  therefore  of  special  importance,  was  in 
error  to  the  extent  of  nearly  40'  (more  than  the  apparent 
breadth  of  the  sun  or  moon),  an  error  which  Hipparchus 
would  have  considered  very  serious.  His  pupil  Rheticus 
(§  74)  reports  an  interesting  discussion  between  his  master 
and  himself,  in  which  the  pupil  urged  the  importance  of 
making  observations  with  all  imaginable  accuracy;  Copper- 
nicus answered  that  minute  accuracy  was  not  to  be  looked 
for  at  that  time,  and  that  a  rough  agreement  between  theory 
and  observation  was  all  that  he  could  hope  to  attain. 
Coppernicus  moreover  points  out  in  more  than  one  place 
that  the  high  latitude  of  Frauenburg  and  the  thickness  of 
the  air  were  so  detrimental  to  good  observation  that,  for 
example,  though  he  had  occasionally  been  able  to  see  the 
planet  Mercury,  he  had  never  been  able  Jo  observe  it 
properly. 

Although  he  published  nothing  of  importance  till  towards 
the  end  of  his  life,  his  reputation  as  an  astronomer  and 
mathematician  appears  to  have  been  established  among 
experts  from  the  date  of  his  leaving  Italy,  and  to  have 
steadily  increased  as  time  went  on. 

In  1515  he  was  consulted  by  a  committee  appointed  by 
the  Lateran  Council  to  consider  the  reform  of  the  calendar, 
which  had  now  fallen  into  some  confusion  (chapter  ji.. 


$  73]  Life  of  Coppernicus  97 

§  22),  but  he  declined  to  give  any  advice  on  the  ground 
that  the  motions  of  the  sun  and  moon  were  as  yet  too 
imperfectly  known  for  a  satisfactory  reform  to  be  possible. 
A  few  years  later  (1524)  he  wrote  an  open  letter,  intended 
for  publication,  to  one  of  his  Cracow  friends,  in  reply  to  a 
tract  on  precession,  in  which,  after  the  manner  of  the  time, 
he  used  strong  language  about  the  errors  of  his  opponent.* 
It  was  meanwhile  gradually  becoming  known  that  he 
held  the  novel  doctrine  that  the  earth  was  in  motion  and 
the  sun  and  stars  at  rest,  a  doctrine  which  was  sufficiently 
startling  to  attrac  t  notice  outside  astronomical  circles. 
About  1531  he  had  the  distinction  of  being  ridiculed  on 
the  stage  at  some  popular  performance  in  the  neighbour- 
hood ;  and  it  is  interesting  to  note  (especially  in  view  of 
the  famous  persecution  of  Galilei  at  Rome  a  century  later) 
that  Luther  in  his  Table  Talk  frankly  described  Coppernicus 
as  a  fool  for  holding  such  opinions,  which  were  obviously 
contrary  to  the  Bible,  and  that  Melanchthon,  perhaps  the 
most  learned  of  the  Reformers,  added  to  a  somewhat  similar 
criticism  a  broad  hint  that  such  opinions  should  not  be 
tolerated.  Coppernicus  appears  to  have  taken  no  notice  of 
these  or  similar  attacks,  and  still  continued  to  publish  nothing. 
No  observation  made  later  than  1529  occurs  in  his  great 
book,  which  seems  to  have  been  nearly  in  its  final  form  by  that 
date ;  and  to  about  this  time  belongs  an  extremely  interest- 
ing paper,  known  as  the  Commentariolus,  which  contains  a 
short  account  of  his  system  of  the  world,  with  some  of  the 
evidence  for  it,  but  without  any  calculations.  It  was 
apparently  written  to  be  shewn  or  lent  to  friends,  and  was 
not  published  ;  the  manuscript  disappeared  after  the  death 
of  the  author  and  was  only  rediscovered  in  1878.  The 
Commentariolus  was  probably  the  basis  of  a  lecture  on 
the  ideas  of  Coppernicus  given  in  1533  by  one  of  the 
Roman  astronomers  at  the  request  of  Pope  Clement  VII. 
Three  years  later  Cardinal  Schomberg  wrote  to  ask 
Coppernicus  for  further  information  as  to  his  views,  the 
letter  showing  that  the  chief  features  were  already  pretty 
accurately  known. 

*  Nullo  demum  loco  ineptior  est  quam  .  .  .  ubi  nim's  pueriliter 
hallucinatur :  Nowhere  is  he  more  foolish  than  .  .  where  he  suffers 
from  delusions  of  too  childish  a  character. 


98  A  Short  History  of  Astronomy  [CH.  IV. 

74.  Similar  requests  must  have  been  made  by  others,  but 
his  final  decision  to  publish  his  ideas  seems  to  have  been 
due  to  the  arrival  at  Frauenburg  in  1539  of  the  enthusiastic 
young  astronomer  generally  known  as  Rheticus.*  Born  in 
1514,  he  studied  astronomy  under  Schoner  at  Niirnberg, 
and  was  appointed  in  1536  to  one  of  the  chairs  of 
mathematics  created  by  the  influence  of  Melanchthon  at 
'Wittenberg,  at  that  time  the  chief  Protestant  University. 

Having  heard,  probably  through  the  Commentariolus^  of 
Coppernicus  and  his  doctrines,  he  was  so  much  interested 
in  them  that  he  decided  to  visit  the  great  astronomer  at 
Frauenburg.  Coppernicus  received  him  with ,  extreme 
kindness,  and  the  visit,  which  was  originally  intended  to 
last  a  few  days  or  weeks,  extended  over  nearly  two  years. 
Rheticus  set  to  work  tq  study  Coppernicus's  manuscript, 
and  wrote  within  a  few  weeks  of  his  arrival  an  extremely 
interesting  and  valuable  account  of  it,  known  as  the  First 
Narrative  (Prima  Narratio),  in  the  form  of  an  open  letter 
to  his  old  master  Schoner,  a  letter  which  was  printed  in  the 
following  spring  and  was  the  first  easily  accessible  account 
of  the  new  doctrines.t 

When  Rheticus  returned  to  Wittenberg,  towards  the  end 
of  1541,  he  took  with  him  a  copy  of  a  purely  mathematical 
section  of  the  great  book,  and  had  it  printed  as  a  textbook 
of  the  subject  (Trigonometry) ;  it  had  probably  been  already 
settled  that  he  was  to  superintend  the  printing  of  the  com- 
plete book  itself.  Coppernicus,  who  was  now  an  old  man 
and  would  naturally  feel  that  his  end  was  approaching,  sent 
the  manuscript  to  his  friend  Giese,  Bishop  of  Kulm,  to  do 
what  he  pleased  with.  Giese  sent  it  at  once  to  Rheticus, 
who  made  arrangements  for  having  it  printed  at  Niirnberg. 
Unfortunately  Rheticus  was  not  able  to  see  it  all  through 
the  press,  and  the  work  had  to  be  entrusted  to  Osiander, 
a  Lutheran  preacher  interested  in  astronomy.  Osiander 

*  His  real  name  was  Georg  Joachim,  that  by  which  he  is  known 
having  been  made  up  by  himself  from  the  Latin  name  of  the  district 
where  he  was  born  (Rhaetia). 

•J"  The  Commcntariolus  and  the  Prima  Narralio  give  most  readers 
a  better  idea  of  what  Coppernicus  did  than  his  larger  book,  in  which 
it  is  comparatively  difficult  to  disentangle  his  leading  ideas  from  the 
mass  of  calculations  based  on  them. 


§§  74,  75]      Publication  of  the  "  De  Revolutionibus "  99 

appears  to  have  been  much  alarmed  at  the  thought  of  the 
disturbance  which  the  heretical  ideas  of  Coppernicus  would 
cause,  and  added  a  prefatory  note  of  his  own  (which  he 
omitted  to  sign),  praising  the  book  in  a  vulgar  way,  and 
declaring  (what  was  quite  contrary  to  the  views  of  the 
author)  that  the  fundamental  principles  laid  down  in  it 
were  merely  abstract  hypotheses  convenient  for  purposes 
of  calculation;  he  also  gave  the  book  the  title  De 
Revolutionibus  Orbium  Celestium  (On  the  Revolutions  of 
the  Celestial  Spheres),  the  last  two  words  of  which  were 
probably  his  own  addition.  The  printing  was  finished  in 
the  winter  1542-3,  and  the  author  received  a  copy  of  his 
book  on  the  day  of  his  death  (May  24th,  1543),  when  his 
memory  and  mental  vigour  had  already  gone. 

75.  The  central  idea  with  which  the  name  of  Coppernicus 
is  associated,  and  which  makes  the  De  Revolutionibus  one 
of  the  most  important  books  in  all  astronomical  literature,  by 
the  side  of  which  perhaps  only  the  Almagest  and  Newton's 
Prindpia  (chapter  ix.,  §§177  seqq.)  can  be  placed,  is  that 
the  apparent  motions  of  the  celestial  bodies  are  to  a  great   \ 
extent  not  real  motions,  but  are  due  to  the  motion  of  the   j 
earth  carrying  the  observer  with  it.     Coppernicus  tells  us    \ 
that  he  had  long  been  struck  by  the  unsatisfactory  nature 
of  the  current  explanations  of  astronomical  observations, 
and  that,  while  searching  in  philosophical  writings  for  some 
better  explanation,  he  had  found  a  reference  of  Cicero  to 
the  opinion  of  Hicetas  that  the  earth  turned  round  on  its 
axis  daily.     Hejfound  similar  views  held  by  other  Pytha- 
goreans, while   Philolaus  and   Aristarchus  of  Samos   had 
also   held    that    the    earth   not   only   rotates,    but   moves 
bodily  round  the  sun  or  some  other  centre  (cf.  chapter  n., 
§  24).     The  opinion  that  the  earth  is  not  the  sole  centre  | 
of  motion,  but  that  Venus  and  Mercury  revolve  round  the  1 
sun,  he  found  to   be  an   old   Egyptian   belief,  supported  1 
also  by  Martianus   Capella^  who  wrote  a  compendium  of 
science  and  philosophy   in   the   5th   or   6th  century  A  D. 
A  more  modern  authority,  Nicholas  of  Cusa  (1401-1464),  a 
mystic  writer  who  refers  to  a  possible  motion  of  the  earth, 
was   ignored  or   not   noticed   by   Coppernicus.      None  of 
the  writers   here   named,  with   the  possible  exception  of 
Aristarchus  of  Samos,  to   whom   Coppernicus   apparently 


ioo  A  Short  History  of  Astronomy  [CH.  IV. 

paid  little  attention,  presented  the  opinions  quoted  as 
more  than  vague  speculations ;  none  of  them  gave  any 
substantial  reasons  for,  much  less  a  proof  of,  their  views  ; 
and  Coppernicus,  though  he  may  have  been  glad,  after  the 
fashion  of  the  age,  to  have  the  support  of  recognised 
authorities,  had  practically  to  make  a  fresh  start  and 
elaborate  his  own  evidence  for  his  opinions. 

It  has  sometimes  been  said  that  Coppernicus  proved 
what  earlier  writers  had  guessed  at  or  suggested ;  it  would 
perhaps  be  truer  to  say  that  he  took  up  certain  floating  ideas, 
which  were  extremely  vague  and  had  never  been  worked 
out  scientifically,  based  on  them  certain  definite  funda- 
mental principles,  and  from  these  principles  developed 
mathematically  an  astronomical  system  which  he  shewed  to 
be  at  least  as  capable  of  explaining  the  observed  celestial 
motions  as  any  existing  variety  of  the  traditional  Ptolemaic 
system.  The  Coppernican  system,  as  it  left  the  hands  of 
the  author,  was  in  fact  decidedly  superior  to  its  rivals  as 
an  explanation  of  ordinary  observations,  an  advantage  which 
it  owed  quite  as  much  to  the  mathematical  skill  with  which 
it  was  developed  as  to  its  first  principles  ;  it  was  in  many 
respects  very  much  simpler;  and  it  avoided  certain 
fundamental  difficulties  of  the  older  system.  It  was  how- 
ever liable  to  certain  serious  objections,  which  were  only 
overcome  by  fresh  evidence  which  was  subsequently 
brought  to  light.  For  the  predecessors  of  Coppernicus 
there  was,  apart  from  variations  of  minor  importance,  but 
one  scientific  system  which  made  any  serious  attempt  to 
account  for  known  facts ;  for  his  immediate  successors  there 
were  two,  the  newer  of  which  would  to  an  impartial  mind 
appear  on  the  whole  the  more  satisfactory,  and  the  further 
study  of  the  two  systems,  with  a  view  to  the  discovery  of 
fresh  arguments  or  fresh  observations  tending  to  support 
the  one  or  the  other,  was  immediately  suggested  as  an 
inquiry  of  .first-rate  importance. 

76.  The  plan  of  the  De  Revolutionibus  bears  a  general 
resemblance  to  that  of  the  Almagest.  In  form  at  least 
the  book  is  not  primarily  an  argument  in  favour  of  the 
motion  of  the  earth,  and  it  is  possible  to  read  much  of 
it  without  ever  noticing  the  presence  of  this  doctrine. 

Coppernicus,  like  Ptolemy,  begins  with  certain  first  prin- 


$$  76,  77]  The  Mot  ion,  of  the  Earth  101 

ciples  or  postulates,  but  on  account  of  their  novelty  takes 
a  little  more  trouble  than  his  predecessor  (cf.  chapter  n., 
§  47)  to  make  them  at  once  appear  probable.  With 
these  postulates  as  a  basis  he  proceeds  to  develop,  by 
means  of  elaborate  and  rather  tedious  mathematical  reason- 
ing, aided  here  and  there  by  references  to  observations, 
detailed  schemes  of  the  various  celestial  motions ;  and  it 
is  by  the  agreement  of  these  calculations  with  observations, 
far  more  than  by  the  general  reasoning  given  at  the 
beginning,  that  the  various  postulates  are  in  effect  justified. 
His  first  postulate,  that  the  universe  is  spherical,  is 
supported  by  vague  and  inconclusive  reasons  similar  to 
those  given  by  Ptolemy  and  others ;  for  the  spherical  form 
of  the  earth  he  gives  several  of  the  usual  valid  arguments, 
one  of  his  proofs  for  its  curvature  from  east  to  west  being 
the  fact  that  eclipses  visible  at  one  place  are  not  visible 
at  another.  A  third  postulate,  that  the  motions  of  the 
celestial  bodies  are  uniform  circular  motions  or  are  com- 
pounded of  such  motions,  is,  as  might  be  expected,  sup- 
ported only  by  reasons  of  the  most  unsatisfactory  character. 
He  argues,  for  example,  that  any  want  of  uniformity  in 
motion 

"must  arise  either  from  irregularity  in  the  moving  power, 
whether  this  be  within  the  body  or  foreign  to  it,  or  from  some 
inequality  of  the  body  in  revolution.  .  .  .  Both  of  which  things 
the  intellect  shrinks  from  with  horror,  it  being  unworthy  to  hold 
such  a  view  about  bodies  which  are  constituted  in  the  most 
perfect  order." 

77.  The  discussion  of  the  possibility  that  the  earth  may 
move,  and  may  even  have  more  than  one  motion,  then 
follows,  and  is  more  satisfactory  though  by  no  means  con- 
clusive. Coppernicus  has  a  firm  grasp  of  the  principle, 
which  Aristotle  had  also  enunciated,  sometimes  known  as 
that  of  relative  motion,  which  he  states  somewhat  as 
follows : — 

"  For  all  change  in  position  which  is  seen  is  due  to  a  motion 
either  of  the  observer  or  of  the  thing,  looked  at,  or  to  changes 
in  the  position  of  both,  provided  that  these  are  different.  For 
when  things  are  moved  equally  relatively  to  the  same  things, 


io2  A  Sfyort  History  of  Astronomy  [CH.  iv. 

no  motion  is  perceived,  as  between  the  object  seen  and   the 
observer."  * 

Coppernicus  gives  no  proof  of  this  principle,  regarding 
it  probably  as  sufficiently  obvious,  when  once  stated,  to 
the  mathematicians  and  astronomers  for  whom  he  was 
writing.  It  is,  however,  so  fundamental  that  it  may  be 
worth  while  to  discuss  it  a  little  more  fully. 

Let,  for  example,  the  observer  be  at  A  and  an  object  at 
B,  then  whether  the  object  move  from  B  to  B',  the  observer 
remaining  at  rest,  or  the  observer  move  an  equal  distance 
in  the  opposite  direction,  from  A  to  A',  the  object  remaining 
at  rest,  the  effect  is  to  the  eye  exactly  the  same,  since  in 

B' 


A' 

FIG.  37. — Relative  motion. 

either  case  the  distance  between  the  observer  and  object 
and  the  direction  in  which  the  object  is  seen,  represented 
in  the  first  case  by  A  B'  and  in  the  second  by  A'  B,  are  the 
same. 

Thus  if  in  the  course  of  a  year  either  the  sun  passes 
successively  through  the  positions  A,  B,  c,  D  (fig.  38),  the 
earth  remaining  at  rest  at  E,  or  if  the  sun  is  at  rest  and 
the  earth  passes  successively  through  the  positions  a,  b,  c,  d, 

*  Omms  enim  quce  videtur  secnndum  locum  mutatio,  aut  est  propter 
locum  muiatio,  aut  est  propter  spectatce  rei  motum,  aut  videntis,  aut 
certe  disparem  utriusque  mutationem.  Nam  inter  wiota  cequaliter 
ad  eadem  non  percipitur  motus,  inter  rem  visam  dico,  et  videntem  (De 
Rev.,  I.  v.). 

I  have  tried  to  remove  some  of  the  crabbedness  of  the  original 
passage  by  translating  freely. 


$  78]  Relative  Motion  103 

at  the  corresponding  times,  the  sun  remaining  at  rest  at  s, 
exactly  the  same  effect  is  produced  on  the  eye,  provided 
that  the  lines  as,  £s,  <rs,  d§  are,  as  in  the  figure,  equal  in 
length  and  parallel  in  direction  to  E  A,  E  B,  E  c,  E  D  re- 
spectively. The  same  being  true  of  intermediate  points, 
exactly  the  same  apparent  effect  is  produced  whether  the 
sun  describe  the  circle  A  B  c  D,  or  the  earth  describe  at 
the  same  rate  the  equal  circle  a  b  c  d.  It  will  be  noticed 
further  that,  although  the  corresponding  motions  in  the 
two  cases  are  at  the  same  times  in  opposite  directions  (as 
at  A  and  a\  yet  each  circle  as  a  whole  is  described, 


b 
FIG.  38. — The  relative  motion  of  the  sun  and  moon. 

as  indicated  by  the  arrow-heads,  in  the  same  direction 
(contrary  to  that  of  the  motion  of  the  hands  of  a  clock, 
in  the  figures  given).  It  follows  in  the  same  sort  of  way 
that  an  apparent  motion  (as  of  a  planet)  may  be  explained 
as  due  partially  to  the  motion  of  the  object,  partially  to 
that  of  the  observer. 

Coppernicus  gives  the  familiar  illustration  of  the 
passenger  in  a  boat  who  sees  the  land  apparently  moving 
away  from  him,  by  quoting  and  explaining  Virgil's  line  :— 

"  Provehimur  portu,  terraeque  urbesque  recedunt." 

78.  The  application  of  the  same  ideas  to  an  apparent 
rotation  round  the  observer,  as  in  the  case  of  the  apparent 
daily  motion  of  the  celestial  sphere,  is  a  little  more  difficult. 
It  must  be  remembered  that  the  eye  has  no  means  of 


104 


A  Short  History  of  Astronomy 


[CH.  IV. 


judging  the  direction  of  an  object  ta'Ken  oy  itself;  it  can 
only  judge  the  difference  between  the  direction  of  the 
object  and  some  other  direction,  whether  that  of  another 
object  or  a  direction  fixed  in  some  way  by  the  body 
of  the  observer.  Thus  when  after  looking  at  a  star  twice 
at  an  interval  of  time  we  decide  that  it  has  moved,  this 
means  that  its  direction  has  changed  relatively  to,  say,  some 
tree  or  house  which  we  had  noticed  nearly  in  its  direction, 
or  that  its  direction  has  changed  relatively  to  the  direction 
in  which  we  are  directing  our  eyes  or  holding  our  bodies. 
Such  a  change  can  evidently  be  interpreted  as  a  change  of 

direction,  either  of  the  star 
or  of  the  line  from  the  eye 
to  the  tree  which  we  used 
as  a  line  of  reference.  To 
apply  this  to  the  case  of  the 
celestial  sphere,  let  us  sup- 
pose that  s  represents  a  star 
on  the  celestial  sphere,  which 
(for  simplicity)  is  overhead 
to  an  observer  on  the  earth 
at  A,  this  being  determined 
by  comparison  with  a  line 
A  B  drawn  upright  on  the 
earth.  Next,  earth  and  ce- 
lestial sphere  being  supposed 
to  have  a  common  centre 
at  o,  let  us  suppose  firstly 

that  the  celestial  sphere  turns  round  (in  the  direction  of 
the  hands  of  a  clock)  till  s  comes  to  s',  and  that  the 
observer  now  sees  the  star  on  his  horizon  or  in  a  direction 
at  right  angles  to  the  original  direction  A  B,  the  angle 
turned  through  by  the  celestial  sphere  being  s  o  s' ;  and 
secondly  that,  the  celestial  sphere  being  unchanged,  the 
earth  turns  round  in  the  opposite  direction,  till  A  B  comes 
to  A'  B',  and  the  star  is  again  seen  by  the  observer  on  hi* 
horizon.  Whichever  of  these  motions  has  taken  place, 
the  observer  sees  exactly  the  same  apparent  motion  in  the 
sky ;  and  the  figure  shews  at  once  that  the  angle  s  o  s' 
through  which  the  celestial  sphere  was  supposed  to  turn 
in  the  first  case  is  equal  to  the  angle  A  o  A'  through  which 


-The  daily  rotation  of 
the  earth. 


$$  7;,  8  ]  The  Motion  of  the  Earth  105 

the  earth  turns  in  the  second  case,  but  that  the  two 
rotations  are  in  opposite  directions.  A  similar  explanation 
evidently  applies  to  more  complicated  cases. 

Hence  the  apparent  daily  rotation  of  the  celestial  sphere 
about  an  axis  through  the  poles  would  be  produced  equally 
well,  either  by  an  actual  rotation  of  this  character,  or  by 
a  rotation  of  the  earth  about  an  axis  also  passing  through 
the  poles,  and  at  the  same  rate,  but  in  the  opposite 
direction,  i.e.  from  west  to  east.  This  is  the  first  motion 
which  Coppernicus  assigns  to  the  earth. 

79.  The  apparent  annual  motion  of  the  sun,  in  accordance 
with  which  it  appears  to  revolve  round  the  earth  in  a  path 
which  is  nearly  a  circle,  can  be  equally  well  explained  by 
supposing  the  sun  to  be  at  rest,  and  the  earth  to  describe 
an  exactly  equal  path  round  the  sun,  the  direction  of  the 
revolution  being  the  same.     This  is  virtually  the   second 
motion  which  Coppernicus  gives  to  the  earth,  though,  on 
account   of  a   peculiarity   in   his   geometrical  method,  he 
resolves  this   motion  into  two  others,  and  combines  with 
one  of  these  a  further  small  motion  which  is  required  for 
precession.* 

80.  Coppernicus's   conception   then    is    that    the   earth 
revolves  round  the  sun  in  the  plane  of  the  ecliptic,  while 
rotating  daily  on  an  axis  which  continually  points  to  the 
poles  of  the  celestial  sphere,  and  therefore  retains  (save  for 
precession)  a  fixed  direction  in  space. 

It  should  be  noticed  that  the  two  motions  thus  assigned 
to  the  earth  are  perfectly  distinct ;  each  requires  its  own 
proof,  and  explains  a  different  set  of  appearances.  It  was 
quite  possible,  with  perfect  consistency,  to  believe  in  one 
motion  without  believing  in  the  other,  as  in  fact  a  very 
few  of  the  16th-century  astronomers  did  (chapter  v.,  §  105). 

In  giving  his  reasons  for  believing  in  the  motion  of  the 

*  To  Coppernicus,  as  to  many  of  his  contemporaries,  as  well  as  to 
the  Greeks,  the  simplest  form  of  a  revolution  of  one  body  round 
another  was  a  motion  in  which  the  revolving  body  moved  as  if 
rigidly  attached  to  the  central  body.  Thus  in  the  case  of  the  earth 
the  second  motion  was  such  that  the  axis  of  the  earth  remained 
inclined  at  a  constant  angle  to  the  line  joining  earth  and  sun,  and 
therefore  changed  its  direction  in  space.  In  order  then  to  make  the 
axis  retain  a  (nearly)  fixed  direction  in  space,  it  was  necessary  to  add 
a  third  motion. 


io6  A  Short  History  of  Astronomy  [CH.  iv. 

earth  Coppernicus  discusses  the  chief  objections  which  had 
been  urged  by  Ptolemy.  To  the  objection  that  if  the  earth 
had  a  rapid  motion  of  rotation  about  its  axis,  the  earth 
would  be  in  danger  of  flying  to  pieces,  and  the  air,  as  well 
as  loose  objects  on  the  surface,  would  be  left  behind,  he 
replies  that  if  such  a  motion  were  dangerous  to  the  solid 
earth,  it  must  be  much  more  so  to  the  celestial  sphere,  which, 
on  account  of  its  vastly  greater  size,  would  have  to  move 
enormously  faster  than  the  earth  to  complete  its  daily 
rotation ;  he  enters  also  into  an  obscure  discussion  of 
difference  between  a  "  natural  "  and  an  "artificial  "  motion, 
of  which  the  former  might  be  expected  not  to  disturb 
anything  on  the  earth. 

Coppernicus  shews  that  the  earth  is  very  small  compared 
to  the  sphere  of  the  stars,  because  wherever  the  observer,, 
is  on  the  earth  the  horizon  appears  to  divide  the  celestial 
sphere  into  two  equal  parts  and  the  observer  appears  always 
to  be  at  the  centre  of  the  sphere,  so  that  any  distance 
through  which  the  observer  moves  on  the  earth  is  im- 
perceptible as  compared  with  the  distance  of  the  stars. 

8 1.  He  goes  on  to  argue  that  the  chief  irregularity  in  the 
motion  of  the  planets,  in  virtue  of  which  they  move  back- 
wards at  intervals  (chapter  i.,  §  14,  and  chapter  n.,  §  51), 
can  readily  be  explained  in  general  by  the  motion  of  the 
earth  and  by  a  motion  of  each  planet  round  the  sun,  in  its 
own  time  and  at  its  own  distance.  From  the  fact  that 
Venus  and  Mercury  were  never  seen  very  far  from  the  sun, 
it  could  be  inferred  that  their  paths  were  nearer  to  the  sun 
than  that  of  the  earth,  Mercury  being  the  nearer  to  the  sun 
of  the  two,  because  never  seen  so  far  from  it  in  the  sky  as 
Venus.  The  other  three  planets,  being  seen  at  times  in  a 
direction  opposite  to  that  of  the  sun,  must  necessarily 
evolve  round  the  sun  in  orbits  larger  than  that  of  the 
earth,  a  view  confirmed  by  the  fact  that  they  were  brightest 
when  opposite  the  sun  (in  which  positions  they  would  be 
nearest  to  us).  The  order  of  their  respective  distances 
from  the  sun  could  be  at  once  inferred  from  the  disturbing 
effects  produced  on  their  apparent  motions  by  the  motion 
of  the  earth  ;  Saturn  being  least  affected  must  on  the  whole 
be  farthest  from  the  earth,  Jupiter  next,  and  Mars  next. 
The  earth  thus  became  one  of  six  planets  revolving  round 


§  80  The  Arrangement  of  the  Solar  System  107 

the  sun,  the  order  of  distance— Mercury,  Venus,  Earth, 
Mars,  Jupiter,  Saturn — being  also  in  accordance  with  the 
rates  of  motion  round  the  sun,  Mercury  performing  its 
revolution  most  rapidly  (in  about  88  days  *),  Saturn  most 
slowly  (in  about  30  years).  On  the  Coppernican  system 


FIG.  40. — The  solar  system  according  to  Coppernicus.     From  the 
De  Revolutionibus. 

the  moon  alone  still  revolved  round  the  earth,  being  the 
only  celestial  body  the  status  of  which  was  substantially 

*  In  this  preliminary  discussion,  as  in  fig.  40,  Coppernicus  gives 
80  days  ;  but  in  the  more  detailed  treatment  given  in  Book  V.  he 
corrects  this  to  88  days. 


io8 


A  Short  History  of  Astronomy 


[CH.    IV. 


unchanged  ;  and  thus  Coppernicus  was  able  to  give  the 
accompanying  diagram  of  the  solar  system  (fig.  40),  repre- 
senting his  view  of  its  general  arrangement  (though  not  of 
the  right  proportions  of  the  different  parts)  and  of  the 
various  motions. 

82.  The  effect  of  the  motion  of  the  earth  round  the  sun 
on   the   length   of  the  day  and  other   seasonal   effects   is 


FIG.  41.  —  Coppernican  explanation  of  the  seasons.     From  the 
De  Revolutionibus. 

discussed  in  some  detail,  and  illustrated  by  diagrams  which 
are  here  reproduced.* 

In  %.  41  A,  B,  c,  D  represent  the  centre  of  the  earth  in  four 
pcsitions/occupied  by  it  about  December  23rd,  March  2ist, 
June  22nd,  and  September  22nd  respectively  (i.e.  at  the 


fig  4 


Fig.  42  has  been  slightly  altered,  so  as  to  make  it  agree  with 


$  82]  The  Seasons,  according  to  Coppernicus  109 

beginnings  of  the  four  seasons,  according  to  astronomical 
reckoning) ;  the  circle  F  G  H  i  in  each  of  its  positions 
represents  the  equator  of  the  earth,  i.e.  a  great  circle  on 
the  earth  the  plane  of  which  is  perpendicular  to  the  axis 
of  the  earth  and  is  consequently  always  parallel  to  the 
celestial  equator.  This  circle  is  not  in  the  plane  of 
the  ecliptic,  but  tilted  up  at  an  angle  of  23!°,  so  that  F 
must  always  be  supposed  below  and  H  above  the  plane  of 
the  paper  (which  represents  the  ecliptic) ;  the  equator  cuts 
the  ecliptic  along  G  i.  The  diagram  (in  accordance  with  the 
common  custom  in  astronomical  diagrams)  represents  the 
various  circles  as  seen  from  the  north  side  of  the  equator 
and  ecliptic.  When  the  earth  is  at  A,  the  north  pole  (as  is 
shewn  more  clearly  in  fig.  42,  in  which  p,  p'  denote  the 
north  pole  and  south  pole  respectively)  is  turned  away 

Partes    Bores. 


Partes  Auftrinae. 

FIG.  42. — Coppernican  explanation  of  the  seasons.     From  the 
De  Revolutionibus. 

from  the  sun,  E,  which  is  on  the  lower  or  south  side  of  the 
plane  of  the  equator,  and  consequently  inhabitants  of  the 
northern  hemisphere  see  the  sun  for  less  than  half  the  day, 
while  those  on  the  southern  hemisphere  see  the  sun  for  more 
than  half  the  day,  and  those  beyond  the  line  K  L  (in  fig.  42) 
see  the  sun  during  the  whole  day.  Three  months  later, 
when  the  earth's  centre  is  at  B  (fig.  41),  the  sun  lies  in  the 
plane  of  the  equator,  the  poles  of  the  earth  are  turned 
neither  towards  nor  away  from  the  sun,  but  aside,  and  all 
over  the  earth  daylight  lasts  for  12  hours  and  night  for  an 
equal  time.  Three  months  later  still,  when  the  earth's 
centre  is  at  c,  the  sun  is  above  the  plane  of  the  equator, 
and  the  inhabitants  of  the  northern  hemisphere  see  the 
sun  for  more  than  half  the  day,  those  on  the  southern 
hemisphere  for  less  than  half,  while  those  in  parts  of  the 
earth  farther  north  than  the  line  M  N  (in  fig.  42)  see  the 
sun  for  the  whole  24  hours.  Finally,  when,  at  the  autumn 


no  A  Short  History  of  Astronomy  [CH.  iv. 

equinox,  the  earth  has  reached  D  (fig.  41),  the  sun  is  again 
in  the  plane  of  the  equator,  and  the  day  is  everywhere  equal 
to  the  night. 

83.  Coppernicus  devotes  the  first  eleven  chapters  of  the 
first  book  to  this  preliminary  sketch  of  his  system ;    the 
remainder  of  this  book  he   fills  with   some   mathematical 
propositions    and   tables,    which,  as   previously  mentioned 
(§  74),  had  already  been  separately  printed  by  Rheticus. 
The  second  book  contains  chiefly  a  number  of  the  usual 
results  relating  to  the   celestial   sphere   and   its   apparent 
daily  motion,  treated  much  as  by  earlier  writers,  but  with 
greater  mathematical  skill.     Incidentally  Coppernicus  gives 
his  measurement  of  the  obl\quity  of  the  ecliptic,  and  infers 
from    a    comparison   with    earlier    observations    that   the 
obliquity  had  decreased,  which  was  in  fact  the  case,  though 
to   a   much   less   extent   than    his   imperfect   observations 
indicated.     The  book  ends  with  a  catalogue  of  stars,  which 
is   Ptolemy's   catalogue,    occasionally   corrected    by    fresh 
observations,  and  rearranged  so  as  to  avoid  the  effects  of 
precession.*      When,  as  frequently  happened,  the   Greek 
and  Latin  versions  of  the  Almagest  gave,  owing  to  copyists' 
or  printers'  errors,  different  results,  Coppernicus  appears  to 
have   followed  sometimes   the   Latin   and   sometimes   the 
Greek  version,  without  in  general  attempting  to  ascertain 
by  fresh  observations  which  was  right. 

84.  The  third  book  begins  with  an  elaborate  discussion 
of  the  precession  of  the  equinoxes  (chapter  n.,  §  42).     From 
a  comparison  of  results  obtained  by  Timocharis,  by  later 
Greek  astronomers,  and  by  Albategnius,  Coppernicus  infers 
that  the  amount   of  precession   has  varied,   but  that   its 
average  value  is  5o"-2  annually  (almost  exactly  the  true 
value),  and  accepts  accordingly  Tabit  ben  Korra's  unhappy 
suggestion   of  the   trepidation   (chapter   lii.,    §   58).      An 
examination  of  the  data  used  by  Coppernicus  shews  that 
the    erroneous    or    fraudulent    observations    of    Ptolemy 
(chapter  11.,  §  50)  are  chiefly  responsible  for  the  perpetua- 
tion of  this  mistake. 

*  Coppernicus,  instead  of  giving  longitudes  as  measured  from  the 
first  point  of  Aries  (or  vernal  equinoctial  point,  chapter  i.,  §§  II,  13), 
which  moves  on  account  of  precession,  measured  the  longitudes  from 
a  standard  fixed  star  (a  Arietis)  not  far  from  this  point. 


$$  83—85]  Precession  .        1 1 1 

Of  much  more  interest  than  the  detailed  discussion  of  tre- 
pidation and  of  geometrical-  schemes  for  representing  it  is 
the  interpretation  of  precession  as  the  result  of  a  motion  of 
the  earth's  axis.  Precession  was  originally  recognised  by 
Hipparchus  as  a  motion  of  the  celestial  equator,  in  which 
its  inclination  to  the  ecliptic  was  sensibly  unchanged. 
Now  the  ideas  of  Coppernicus  make  the  celestial  equator 
dependent  on  the  equator  of  the  earth,  and  hence  on  its 
axis ;  it  is  in  fact  a  great  circle  of  the  celestial  sphere 
which  is  always  perpendicular  to  the  axis  about  which  the 
earth  rotates  daily.  Hence  precession,  en  the  theory  of 
Coppernicus,  arises  from  a  slow  motion  of  the  axis  of  the 
earth,  which  moves  so  as  always  to  remain  inclined  at  the 
same  angle  to  the  ecliptic,  and  to  return  to  its  original 
position  after  a  period  of  about  26,000  years  (since  a 
motion  of  5o"'2  annually  is  equivalent  to  360°  or  a  complete 
circuit  in  that  period) ;  in  other  words,  the  earth's  axis 
has  a  slow  conical  motion,  the  central  line  (or  axis)  of  the 
cone  being  at  right  angles  to  the  plane  of  the  ecliptic. 

85.  Precession  being  dealt  with,  the  greater  part  of  the 
remainder  of  the  third  book  is  devoted  to  a  discussion  in 
detail  of  the  apparent  annual  motion  of  the  sun  round  the 
earth,  corresponding  to  the  real  annual  motion  of  the  earth 
round  the  sun.  The  geometrical  theory  of  the  Almagest 
was  capable  of  being  immediately  applied  to  the  new  system, 
and  Coppernicus,  like  Ptolemy,  uses  an  eccentric.  He 
makes  the  calculations  afresh,  arrives  at  a  smaller  and  more 
accurate  value  of  the  eccentricity  (about  ^T  instead  of  -^j), 
fixes  the  position  of  the  apogee  and  perigee  (chapter  n.,  §  39), 
or  rather  of  the  equivalent  aphelion  and  peiihelion  (i.e.  the 
points  in  the  earth's  orbit  where  it  is  respectively  farthest 
from  and  nearest  to  the  sun),  and  thus  verifies  Albategnius's 
discovery  (chapter  in.,  §  59)  of  the  motion  of  the  line  of 
apses.  The  theory  of  the  earth's  motion  is  worked  out  in 
some  detail,  and  tables  are  given  whereby  the  apparent  place 
of  the  sun  at  any  time  can  be  easily  computed. 

The  fourth  book  deals  with  the  theory  of  the  moon.  As 
has  been  already  noticed,  the  moon  was  the  only  celestial 
b')dy  the  position  of  which  in  the  universe  was  substantially 
unchanged  by  Coppernicus,  and  it  might  hence  have  been 
expected  that  little  alteration  would  have  been  required  in 


ii2  A  Short  History  of  Astronomy  [CH.  iv. 

the  traditional  theory.  Actually,  however,  there  is  scarcely 
any  part  of  the  subject  in  which  Coppernicus  did  more  to 
diminish  the  discrepancies  between  theory  and  observation. 
He  rejects  Ptolemy's  equant  (chapter  n.,  §  51),  partly  on 
the  ground  that  it  produces  an  irregular  motion  unsuitable 
for  the  heavenly  bodies,  partly  on  the  more  substantial 
ground  that,  as  already  pointed  out  (chapter  u.,  §  48), 
Ptolemy's  theory  makes  the  apparent  size  of  the  moon  at 
times  twice  as  great  as  at  others.  By  an  arrangement  of 
epicycles  Coppernicus  succeeded  in  representing  the  chief 
irregularities  in  the  moon's  motion,  including  evection,  but 
without  Ptolemy's  prosneusis  (chapter  IL,  §  48)  or  Abul 
•Wafa's  inequality  (chapter  in.,  §  60),  while  he  made  the 
changes  in  the  moon's  distance,  and  consequently  in  its 
apparent  size,  not  very  much  greater  than  those  which 
actually  take  place,  the  difference  being  imperceptible  by 
the  rough  methods  of  observation  which  he  used.* 

In  discussing  the  distances  and  sizes  of  the  sun  and 
moon  Coppernicus  follows  Ptolemy  closely  (chapter  n.,  §  49 ; 
cf.  also  fig.  20) ;  he  arrives  at  substantially  the  same  estimate 
of  the  distance  of  the  moon,  but  makes  the  sun's  distance 
1,500  times  the  earth's  radius,  thus  improving  to  some  extent 
on  the  traditional  estimate,  which  was  based  on  Ptolemy's. 
He  also  develops  in  some  detail  the  effect  of  parallax  on 
the  apparent  place  of  the  moon,  and  the  variations  in  the 
apparent  size,  owing  to  the  variations  in  distance  :  and  the 
book  ends  with  a  discussion  of  eclipses. 
^  86.  The  last  two  books  (V.  and  VI.)  deal  at  length  with 
me  motion  of  the  planets. 

In  the  cases  of  Mercury  and  Venus,  Ptolemy's  explana- 
tion of  the  motion  could  with  little  difficulty  be  rearranged 
so  as  to  fit  the  ideas  of  Coppernicus.  We  have  seen 
(chapter  IL,  §51)  that,  minor  irregularities  being  ignored, 
the  motion  of  either  of  these  planets  could  be  represented 
by  means  of  an  epicycle  moving  on  a  deferent,  the  centre  of 

*  According  to  the  theory  of  Coppernicus,  the  diameter  of  the 
moon  when  greatest  was  about  \  greater  than  its  average  amount; 
modern  observations  make  this  fraction  about  T\.  Or,  to  put  it  other- 
wise, the  diameter  of  the  moon  when  greatest  ought  to  exceed  its 
value  when  least  by  about  8'  according  to  Coppernicus,  and  by  about  5' 
according  to  modern  observations. 


86] 


The  Motion  of  the  Planets 


the  epicycle  being  always  in  the  direction  of  the  sun,  the 
ratio  of  the  sizes  of  the  epicycle  and  deferent  being  fixed, 
but  the  actual  dimensions  being  practically  arbitrary. 
Ptolemy  preferred  on  the  whole  to  regard  the  epicycles  of 
both  these  planets  as  lying  between  the  earth  and  the  sun. 
The  idea  of  making  the  sun  a  centre  of  motion  having  once 
been  accepted,  it  was  an  obvious  simplification  to  make 
the  centre  of  the  epicycle  not  merely  lie  in  the  direction 
of  the  sun,  but  actually  be  the  sun.  In  fact,  if  the  planet 


FIG.  43. — The  orbits  of  Venus  and  of  the  earth. 

in  question  revolved  round  the  sun  at  the  proper  distance 
and  at  the  proper  rate,  the  same  appearances  would  be 
produced  as  by  Ptolemy's  epicycle  and  deferent,  the  path 
of  the  planet  round  the  sun  replacing  the  epicycle,  and  the 
app'arent  path  of  the  sun  round  the  earth  (or  the  path  of 
the  earth  round  the  sun)  replacing  the  deferent. 

In  discussing  the  time  of  revolution  of  a  planet  a  dis- 
tinction has  to  be  made,  as  in  the  case  of  the  moon  (chap- 
ter ii.,  §  40),  between  the  synodic  and  sidereal  periods  of 
revolution.  Venus,  for  example,  is  seen  as  an  evening  star 

8 


A  Short  History  of  Astronomy 


[CH.    IV. 


at  its  greatest  angular  distance  from  the  sun  (as  at  v  in 
fig.  43)  at  intervals  of  about  584  days.  This  is  therefore 
the  time  which  Venus  takes  to  return  to  the  same  position 
relatively  to  the  sun,  as  seen  from  the  earth,  or  relatively 
to  the  earth,  as  seen  from  the  sun ;  this  time  is  called 
the  synodic  period.  But  as  during  this  time  the  line  E  s 
has  changed  its  direction,  Venus  is  no  longer  in  the 
same  position  relatively  to  the  stars,  as  seen  either  from 
the  sun  or  from  the  earth.  If  at  first  Venus  and  the 


FIG.  44. — The  synodic  and  sidereal  periods  of  Venus. 

earth  are  at  v,,  EJ  respectively,  after  584  days  (or  about 
a  year  and  seven  months)  the  earth  will  have  performed 
rather  more  than  a  revolution  and  a  half  round  the 
sun  and  will  be  at  E.,;  Venus  being  again  at  the  greatest 
distance  from  the  sun  will  therefore  be  at  v2,  but  will 
evidently  be  seen  in  quite  a  different  part  of  the  sky, 
and  will  not  h  *ve  performed  an  exact  revolution  round  the 
sun.  It  is  important  to  know  how  long  the  line  s  vl  takes 
to  return  to  the  same  position,  i.e.  how  long  Venus  takes 
to  return  to  the  same  position  with  respect  to  the  stars, 


§  87]  The  Motion  of  the  Planets  115 

as  seen  from  the  sun,  an  interval  of  time  known  as  the 
sidereal  period.  This  can  evidently  be  calculated  by  a 
simple  rule-of-three  sum  from  the  data  given.  For  Venus 
has  in  584  days  gained  a  complete  revolution  on  the 
earth,  or  has  gone  as  far  as  the  earth  would  have  gone  in 
584  +  365  or  949  days  (fractions  of  days  being  omitted  for 
simplicity) ;  hence  Venus  goes  in  584  x  fff  days  as  far 
as  the  earth  in  365  days,  i.e.  Venus  completes  a  revolution 
in  584  x  |f|  or  225  days.  This  is  therefore  the  sidereal 
period  of  Venus.  The  process  used  by  Coppernicus  was ' 
different,  as  he  saw  the  advantage  of  using  a  long  period  of 
time,  so  as  to  diminish  the  error  due  to  minor  irregularities, 
and  he  therefore  obtained  two  observations  of  Venus  at 
a  considerable  interval  of  time,  in  which  Venus  occupied 
very  nearly  the  same  position  both  with  respect  to  the  sun 
and  to  the  stars,  so  that  the  interval  of  time  contained  very 
nearly  an  exact  number  of  sidereal  periods  as  well  as  of 
synodic  periods.  By  dividing  therefore  the  observed 
interval  of  time  by  the  number  of  sidereal  periods  (which 
being  a  whole  number  could  readily  be  estimated),  the 
sidereal  period  was  easily  obtained.  A  similar  process 
shewed  that  the  synodic  period  of  Mercury  was  about  116 
days,  and  the  sidereal  period  about  88  days. 

The  comparative  sizes  of  the  orbits  of  Venus  and 
Mercury  as  compared  with  that  of  the  earth  could  easily 
be  ascertained  from  observations  of  the  position  of  either 
planet  when  most  distant  from  the  sun.  Venus,  for 
example,  appears  at  its  greatest  distance  from  the  sun  when 
at  a  point  vt  (fig.  44)  such  that  Vj  E,  touches  the  circle  in 
which  Venus  moves,  and  the  angle  E,  v,  s  is  then  (by 
a  known  property  of  a  circle)  a  right  angle.  The  angle 
s  Et  VL  being  observed,  the  shape  of  the  triangle  s  E,  vx  is 
known,  and  the  ratio  of  its  sides  can  be  readily  calculated. 
Thus  Coppernicus  found  that  the  average  distance  of 
Venus  from  the  sun  was  about  72  and  that  of  Mercury 
about  36,  the  distance  of  the  earth  from  the  sun  being 
taken  to  be  100;  the  corresponding  modern  figures  are 
72-3  and  387. 

87.  In  the  case  of  the  superior  planets,  Mars,  Jupiter, 
and  Saturn,  it  was  much  more  difficult  to  recognise  that 
their  motions  could  be  explained  by  supposing  them  to 


n6 


A  Short  History  of  Astronomy 


[CH.    IV. 


revolve  round  the  sun,  since  the  centre  of  the  epicycle 
did  not  always  lie  in  the  direction  of  the  sun,  but  might 
be  anywhere  in  the  ecliptic.  One  peculiarity,  however, 
in  the  motion  of  any  of  the  superior  planets  might  easily 
have  suggested  their  motion  round  the  sun,  and  was  either 
completely  overlooked  by  Ptolemy  or  not  recognised  by 
him  as  important.  It  is  possible  that  it  was  one  of  the 
clues  which  led  Coppernicus  to  his  system.  This  peculi- 
arity is  that  the  radius  of  the  epicycle  of  the  planet, 
/j,  is  always  parallel  to  the  line  ES  joining  the  earth 
and  sun,  and  consequent^  performs  a  complete  re- 
volution in  a  year.  This 
connection  between  the 
motion  of  the  planet  and 
that  of  the  sun  received 
no  explanation  from 
Ptolemy's  theory.  Now 
if  we  draw  E  j'  parallel 
to  j  j  and  equal  to  it  in 


FIG.  45. — The  epicycle  of  Jupiter. 


length,  it  is  easily  seen  * 
that  the  line  j'  j  is  equal 
and  parallel  to  E/,  that 
consequently  j  describes 
a  circle  round  j'  just  as 
j  round  E.  Hence  the 
motion  of  the  planet  can 
equally  well  be  repre- 
sented by  supposing  it  to  move  in  an  epicycle  (represented 
by  the  large  dotted  circle  in  the  figure)  of  which  j'  is  the 
centre  and  j'  j  the  radius,  while  the  centre  of  the  epicycle, 
remaining  always  in  the  direction  of  the  sun,  describes 
a  deferent  (represented  by  the  small  circle  round  E)  of  which 
the  earth  is  the  centre.  By  this  method  of  representation 
the  motion  of  the  superior  planet  is  exactly  like  that  of 
an  inferior  planet,  except  that  its  epicycle  is  larger  than 
its  deferent ;  the  same  reasoning  as  before  shows  that  the 
motion  can  be  represented  simply  by  supposing  the  centre 
j'  of  the  epicycle  to  be  actually  the  sun.  Ptolemy's  epicycle 
and  deferent  are  therefore  capable  of  being  replaced,  with- 
out affecting  the  position  of  the  planet  in  the  sky,  by  a 
*  Euclid,  i.  33. 


37J 


The  Motion  of  the  Planets 


117 


motion  of  the  planet  in  a  circle  round  the  sun,  while  the 
sun  moves  round  the  earth,  or,  more  simply,  the  earth 
round  the  sun. 

The  synodic  period  of  a  superior  planet  could  best  be 
determined  by  observing  when  the  planet  was  in  opposition, 
i.e.  when  it  was  (nearly)  opposite  the  sun,  or,  more 
accurately  (since  a  planet  does  not  move  exactly  in  the 
ecliptic),  when  the  longitudes  of  the  planet  and  sun  differed 
by  1 80°  (or  two  right  angles,  chapter  n.,  §  43).  The 


FIG.  46. — The  relative  sizes  of  the  orbits  ot  the  earth  and  of  a 
superior  planet. 

sidereal  period  could  then  be  deduced  nearly  as  in  the  case 
of  an  inferior  planet,  with  this  difference,  that  the  superior 
planet  moves  more  slowly  than  the  earth,  and  therefore  loses 
one  complete  revolution  in  each  synodic  period  ;  or  the 
sidereal  period  might  be  found  as  before  by  observing 
when  oppositions  occurred  nearly  in  the  same  part  of  the 
sky.*  Coppernicus  thus  obtained  very  fairly  accurate 

*  If  p  be  the  synodic  period   of  a   planet  (in  years),  and   s  the 
sidereal  period,  then  we  evidently  have   -  +   I   =  -    for  an  inferior 

II  F  S 

planet,  and  I   -  —  =  -  for  a  superior  planet. 


1 1 8  A  Short  History  of  Astronomy  [Cn.  IV. 

values  for  the  synodic  and  sidereal  periods,  viz.  780  days 
and  687  days  respectively  for  Mars,  399  days  and  about 
12  years  for  Jupiter,  378  days  and  30  years  for  Saturn 
(cf.  fig.  40). 

The  calculation  of  the  distance  of  a  superior  planet 
from  the  sun  is  a  good  deal  more  complicated  than  that 
of  Venus  or  Mercury.  If  we  ignore  various  details,  the 
process  followed  by  Coppernicus  is  to  compute  the  position 
of  the  planet  as  seen  from  the  sun,  and  then  to  notice 
when  this  position  differs  most  from  its  position  as  seen 
from  the  earth,  i.e.  when  the  earth  and  sun  are  farthest  apart 
as  seen  from  the  planet.  This  is  clearly  when  (fig.  46) 
the  line  joining  the  planet  (p)  to  the  earth  (E)  touches  the 
circle  described  by  the  earth,  so  that  the  angle  s  P  E  is 
then  as  great  as  possible.  The  angle  p  E  s  is  a  right 
angle,  and  the  angle  s  P  E  is  the  difference  between  the 
observed  place  of  the  planet  and  its  computed  place  as 
seen  from  the  sun ;  these  two  angles  being  thus  known,  the 
shape  of  the  triangle  s  P  E  is  known,  and  therefore  also 
the  ratio  of  its  sides.  In  this  way  Coppernicus  found 
the  average  distances  of  Mars,  Jupiter,  and  Saturn  from  the 
sun  to  be  respectively  about  i|,  5,  and  9  times  that  of  the 
earth;  the  corresponding  modern  figures  are  1*5,  5*2,  9'5. 

88.  The  explanation  of  the  stationary  points  of  the 
planets  (chapter  i.,  §  14)  is  much  simplified  by  the  ideas  of 
Coppernicus.  If  we  take  first  an  inferior  planet,  say  Mercury 
(fig.  47),  then  when  it  lies  between  the  earth  and  sun,  as 
at  M  (or  as  on  Sept.  5  in  fig.  7),  both  the  earth  and  Mer- 
cury are  moving  in  the  same  direction,  but  a  comparison 
of  the  sizes  of  the  paths  of  Mercury  and  the  earth,  and  of 
their  respective  times  of  performing  complete  circuits,  shews 
that  Mercury  is  moving  faster  than  the  earth.  Consequently 
to  the  observer  at  E,  Mercury  appears  to  be  moving  from 
left  to  right  (in  the  figure),  or  from  east  to  west ;  but  this 
is  contrary  to  the  general  direction  of  motion  of  the  planets, 
i.e.  Mercury  appears  to  be  retrograding.  On  the  other 
hand,  when  Mercury  appears  at  the  greatest  distance  from 
the  sun,  as  at  M,  and  M,,  its  own  motion  is  directly  towards 
or  away  from  the  earth,  and  is  therefore  imperceptible ; 
but  the  earth  is  moving  towards  the  observer's  right,  and 
therefore  Mercury  appears  to  be  moving  towards  the  left, 


88] 


Stationary  Points 


119 


or  from  west  to  east.  Hence  between  M,  and  M  its  motion 
has  changed  from  direct  to  retrograde,  and  therefore  at 
some  intermediate  point,  say  ;;/,  (about  Aug.  23  in  fig.  7), 
Mercury  appears  for  the  moment  to  be  stationary,  and 
similarly  it  appears  to  be  stationary  again  when  at  some  point 
m.2  between  M  and  MB  (about  Sept  13  in  fig.  7). 

In  the  case  of  a  superior  planet,  say  Jupiter,  the  argument 


FIG.  47. — The  stationary  points  of  Mercury. 

is  nearly  the  same.  When  in  opposition  at  j  (as  on 
Mar.  26  in  fig.  6),  Jupiter  moves  more  slowly  than  the 
earth,  and  in  the  same  direction,  and  therefore  appears  to 
be  moving  in  the  opposite  direction  to  the  earth,  i.e.  as  seen 
from  E  (fig.  48),  from  left  to  right,  or  from  east  to  west,  that 
is  in  the  retrograde  direction.  But  when  Jupiter  is  in 
either  of  the  positions  j,  or  j  (in  which  the  earth  appears 
to  the  observer  on  Jupiter  to  be  at  its  greatest  distance 


120 


A  Short  History  of  Astronomy 


[CH.  IV. 


from  the  sun),  the  motion  of  the  earth  itself  being  directly 
to  or  from  Jupiter  produces  no  effect  on  the  apparent 
motion  of  Jupiter  (since  any  displacement  directly  to  or 
from  the  observer  makes  no  difference  in  the  object's 
place  on  the  celestial  sphere) ;  but  Jupiter  itself  is  actually 
moving  towards  the  left,  and  therefore  the  motion  of 

Jo       


FIG.  48.— The  stationary  points  of  Jupiter. 

Jupiter  appears  to  be  also  from  right  to  left,  or  from  west 
to  east.  Hence,  as  before,  between  j,  and  j  and  between 
j  and  J2  there  must  be  points  /„  /2  (Jan.  24  and  May  27, 
in  fig.  6)  at  which  Jupiter  appears  for  the  moment  to  be 
stationary. 

The  actual  discussion  of  the  stationary  points  given  by 
Coppernicus  is  a  good  deal  more  elaborate  and  more 
technical  than  the  outline  given  here,  as  he  not  only  shews 


$$89,90]  The  Motion  of  the  Planets  121 

that  the  stationary  points  must  exist,  but    shews  how  to 
calculate  their  exact  positions. 

89.  So   far    the   theory   of  the   planets   has   cnly   been 
sketched  very  roughly,  in  order  to  bring  into  prominence 
the  essential  differences  between  the  Coppernican  and  the 
Ptolemaic  explanations  of  their  motions,   and   n.>  account 
has  been  taken  of  the  minor  irregularities  for  which  Ptolemy 
devised  his  system  of  equants,  eccentrics,  etc.,  nor  of  the 
motion  in  latitude,  i.e.  to  and  from  the  ecliptic.     Copper- 
nicus,  as  already  mentioned,  rejected  the  equant,  as  beir.j 
productive  of  an  irregularity  "  unworthy  "  of  the  celestial 
bodies,  and  constructed  for  each  planet  a  fairly  complicated 
system    of   epicycles.      For    the    motion    in    latitude    dis- 
cussed in  Book  VI.  he  supposed  the  orbit  of  each  planet 
round  the  sun  to  be  inclined  to  the  ecliptic  at  a  small 
angle,  different  for  each  planet,  but  found  it  necessary,  in 
order  that  his  theory   should   agree   with   observation,    to 
introduce  the  wholly  imaginary  complication  of  a  regular 
increase  and  decrease  in  the  inclinations  of  the  orbits  of 
the  planets  to  the  ecliptic. 

The  actual  details  of  the  epicycles  employed  are  of  no 
great  interest  now,  but  it  may  be  worth  while  to  notice  that 
for  the  motions  of  the  moon,  earth,  and  five  other  planets 
Coppernicus  required  altogether  34  circles,  viz.  four  for  the 
moon,  three  for  the  earth,  seven  for  Mercury  (the  motion 
of  which  is  peculiarly  irregular),  and  five  for  each  of  the 
other  planets  ;  this  number  being  a  good  deal  less  than 
that  required  in  most  versions  of  Ptolemy's  system : 
Fracastor  (chapter  in.,  §  69),  for  example,  writing  in  1538, 
required  79  spheres,  of  which  six  were  required  for  the 
fixed  stars. 

90.  The   planetary   theory   of    Coppernicus    necessarily 
suffered  from  one  of  the  essential  defects  of  the  system  of 
epicycles.     It  is,  in  fact,  always  possible  to  choose  a  system 
of  epicycles  in  such  a  way  as  to  make  either  the  direction  of 
any  body  or  its  distance  vary  in  any  required  manner,  but 
not  to  satisfy  both  requirements  at  once.     In  the  case  of  the 
motion  of  the  moon  round  the  earth,  or  of  the  earth  round 
the  sun,  cases  in  which  variations   in   distance  could  not 
readily  be  observed,  epicycles  might  therefore  be  expected 
to  give  a  satisfactory  result,  at  any  rate  until  methods  gf 


122  A  Short  History  of  Astronomy  [CH.  iv. 

observation  were  sufficiently  improved  to  measure  with  some 
accuracy  the  apparent  sizes  of  the  sun  and  moon,  and  so 
check  the  variations  in  their  distances.  But  any  variation 
in  the  distance  of  the  earth  from  the  sun  would  affect  not 
merely  the  distance,  but  also  the  direction  in  which  a  planet 
would  be  seen ;  in  the  figure,  for  example,  when  the  planet 
is  at  P  and  the  sun  at  s,  the  apparent  position  of  the  planet, 
as  seen  from  the  earth,  will  be  different  according  as  the 
earth  is  at  E  or  E'.  Hence  the  epicycles  and  eccentrics  of 
Coppernicus,  which  had  to  be  adjusted  in  such  a  way  that 


E         E'  S 

FIG.  49. — The  alteration  in  a  planet's  apparent  position  due  to  an 
alteration  in  the  earth's  distance  from  the  sun. 

they  necessarily  involved  incorrect  values  of  the  distances 
between  the  sufi  and  earth,  gave  rise  to  corresponding 
errors  in  the  observed  places  of  the  planets.  The  obser- 
vations which  Coppernicus  used  were  hardly  extensive  or 
accurate  enough  to  show  this  discrepancy  clearly ;  but  a 
crucial  test  was  thus  virtually  suggested  by  means  of  which, 
when  further  observations  of  the  planets  had  been  made, 
a  decision  could  be  taken  between  an  epicyclic  representa- 
tion of  the  motion  of  the  planets  and  some  other  geometrical 
scheme. 
.  91.  The  merits  of  Coppernicus  are  so  great,  and  the  part 


§$  9i,  gz]  The   Use  of  Epicycles  by  Coppernicus  123 

which  he  played  in  the  overthrow  of  the  Ptolemaic  system 
is  so  conspicuous,  that  we  are  sometimes  liable  to  forget 
that,  so  far  from  rejecting  the  epicycles  and  eccentrics  of 
the  Greeks,  he  used  no  other  geometrical  devices,  and  was 
even  a  more  orthodox  "  epicyclist "  than  Ptolemy  himself, 
as  he  rejected  the  equants  of  the  latter.*  Milton's  famous 
description  (Par.  Lost,  VIII.  82-5)  of 

"The  Sphere 

With  Centric  and  Eccentric  scribbled  o'er, 
Cycle  and  Epicycle,  Orb  in  Orb," 

applies  therefore  just  as  well  to  the  astronomy  of  Copper- 
nicus as  to  that  of  his  predecessors ;  and  it  was  Kepler 
(chapter  vn.),  writing  more  than  half  a  century  later,  not 
Coppernicus,  to  whom  the  rejection  of  the  epicycle  and 
eccentric  is  due. 

92.  One  point  which  was  of  importance  in  later 
controversies  deserves  special  mention  here.  The  basis 
of  the  Coppernican  system  was  that  a  motion  of  the 
earth  carrying  the  observer  with  it  produced  an  apparent 
motion  of  other  bodies.  The  apparent  motions  of  the 
sun  and  planets  were  thus  shewn  to  be  in  great  part 
explicable  as  the  result  of  the  motion  of  the  earth  round 
the  sun.  Similar  reasoning  ought  apparently  to  lead 
to  the  conclusion  that  the  fixed  stars  would  also  appear 
to  have  an  annual  motion.  There  would,  in  fact,  be  a 
displacement  of  the  apparent  position  of  a  star  due  to 
the  alteration  of  the  earth's  position  in  its  orbit,  closely 
resembling  the  alteration  in  the  apparent  position  of  the 
moon  due  to  the  alteration  of  the  observer's  position 
on  the  earth  which  had  long  been  studied  under  the  name 
of  parallax  (chapter  IL,  §  43).  As  such  a  displacement 
had  never  been  observed,  Coppernicus  explained  the 
apparent  contradiction  by  supposing  the  fixed  stars  so 

*  Recent  biographers  have  called  attention  to  a  cancelled  passage 
in  the  manuscript  of  the  De  Revolutionibus  in  which  Coppernicus 
shews  that  an  ellipse  can  be  generated  by  a  combination  of  circular 
motions.  The  proposition  is,  however,  only  a  piece  of  pure  mathe- 
matics, and  has  no  relation  to  the  motions  of  the  planets  round  the 
sun.  It  cannot,  therefore,  fairly  be  regarded  as  in  any  way  an 
anticipation  of  the  ideas  of  Kepler  (chapter  vn.). 


124 


A  Short  History  of  Astronomy        CH.  i  v , 


92 


far  off  that  any  motion  due  to  this  cause  was  too  small 
to  be  noticed.  If,  for  example,  the  earth  moves  in  six 
months  from  E  to  E',  the  change  in  direction  of  a  star  at 
s'  is  the  angle  E'  s'  E,  which  is  less  than  that  of  a  nearer 
star  at  s ;  and  by  supposing  the  star  s'  sufficiently  remote, 
the  angle  E'  s'  E  can  be  made  as  small  as  may  be  required. 
For  instance,  if  the  distance  of  the  star  were  300  times 
the  distance  E  E',  i.e.  600  times  as  far  from  the  earth  as 


FIG.  50. — Stellar  parallax. 

the  sun  is,  the  angle  E  s'  E'  would  be  less  than  1 2', 
a  quantity  which  the  instruments  of  the  time  were  barely 
capable  of  detecting.*  But  more  accurate  observations 
of  the  fixed  stars  might  be  expected  to  throw  further  light 
on  this  problem. 

i 

*  It  may  be  noticed  that  the  differential  method  of  parallax 
(chapter  vi.,  §  129),  by  which  such  a  quantity  as  12'  could  have 
been  noticed,  was  put  out  of  court  by  the  general  supposition,  shared 
by  Coppernicus,  that  the  stars  were  all  at  the  same  distance  from 
us. 


CHAPTER  V. 

THE    RECEPTION    OF    THE    COPPERNICAN    THEORY    AND   THE 
PROGRESS    OF    OBSERVATION. 

"  Preposterous  wits  that  cannot  row  at  ease 
On  the  smooth  channel  of  our  common  seas; 
And  such  are  those,  in  my  conceit  at  least, 
Those  clerks  that  think — think  how  absurd  a  jest ! 
That  neither  heavens  nor  stars  do  turn  at  all, 
Nor  dance  about  this  great  round  Earthly  Ball, 
But  the  Earth  itself,  this  massy  globe  of  ours, 
Turns  round  about  once  every  twice  twelve  hours !  " 

Du  BARTAS  (Sylvester's  trans1ation\ 

93.  THE  publication  of  the  De  Revolutionibus  appears  to 
have  been  received  much  more  quietly  than  might  have 
been  expected  from  the  startling  nature  of  its  contents. 
The  book,  in  fact,  was  so  written  as  to  be  unintelligible  except 
to  mathematicians  of  considerable  knowledge  and  ability, 
and  could  not  have  been  read  at  all  generally.  Moreover 
the  preface,  inserted  by  Osiander  but  generally  supposed 
to  be  by  the  author  himself,  must  have  done  a  good  deal 
to  disarm  the  hostile  criticism  due  to  prejudice  and  custom, 
by  representing  the  fundamental  principles  of  Coppernicus 
as  mere  geometrical  abstractions,  convenient  for  calcu- 
lating the  celestial  motions.  Although,  as  we  have  seen 
(chapter  iv.,  §  73),  the  contradiction  between  the  opinions 
of  Coppernicus  and  the  common  interpretation  of  various 
passages  in  the  Bible  was  promptly  noticed  by  Luther, 
Melanchthon,  and  others,  no  objection  was  raised  either 
by  the  Pope  to  whom  the  book  was  dedicated,  or  by  his 
immediate  successors. 

The  enthusiastic  advocacy  of  the  Coppernican  views  by 
Rheticus  has  already  been  referred  to.     The  only  other 

125 


126  A  Short  History  of  Astronomy  [CH.  V. 

astronomer  of  note  who  at  once  accepted  the  new  views 
was  his  friend  and  colleague  Erasmus  Reinhold  (born 
at  Saalfeld  in  1511),  who  occupied  the  chief  chair  of 
mathematics  and  astronomy  at  Wittenberg  from  1536  to 
1553,  and  it  thus  happened,  curiously  enough,  that  the 
doctrines  so  emphatically  condemned  by  two  of  the  great 
Protestant  leaders  were  championed  principally  in  what 
was  generally  regarded  as  the  very  centre  of  Protestant 
thought. 

94.  Rheticus,  after  the  publication  of  the  Narratio 
Prima  and  of  an  Ephemeris  or  Almanack  based  on 
Coppernican' principles  (1550),  occupied  himself  principally 
with  the  calculation  of  a  very  extensive  set  of  mathematical 
tables,  which  he  only  succeeded  in  finishing  just  before  his 
death  in  1576. 

Reinhold  rendered  to  astronomy  the  extremely  important 
service  of  calculating,  on  the  basis  of  the  De  Revolutionibus, 
tables  of  the  motions  of  the  celestial  bodies,  which  were 
published  in  1551  at  the  expense  of  Duke  Albert  of  Prussia 
and  hence  called  Tabula  Prutenicce,  or  Prussian  Tables. 
Reinhold  revised  most  of  the  calculations  made  by  Copper- 
nicus,  whose  arithmetical  work  was  occasionally  at  fault; 
but  the  chief  object  of  the  tables  was  the  development  in 
great  detail  of  the  work  in  the  De  Revolutionibus,  in  such 
a  form  that  the  places  of  the  chief  celestial  bodies  at  any 
required  time  could  be  ascertained  with  ease.  The  author 
claimed  for  his  tables  that  from  them  the  places  of  all  the 
heavenly  bodies  could  be  computed  for  the  past  3,000  years, 
and  would  agree  with  all  observations  recorded  during  that 
period.  The  tables  were  indeed  found  to  be  on  the  whole 
decidedly  superior  to  their  predecessors  the  Alfonsine 
Tables  (chapter  in.,  §  66),  and  gradually  came  more  and 
more  into  favour,  until  superseded  three-quarters  of  a  cen- 
tury later  by  the  Rudolphine  Tables  of  Kepler  (chapter  vn., 
§  148).  This  superiority  of  the  new  tables  was  only 
indirectly  connected  with  the  difference  in  the  principles 
on  which  the  two  sets  of  tables  were  based,  and  was  largely 
due  to  the  facts  that  Reinhold  was  a  much  better  computer 
than  the  assistants  of  Alfonso,  and  that  Coppernicus,  if 
not  a  better  mathematician  than  Ptolemy,  at  any  rate  had 
better  mathematical  tools  at  command.  Nevertheless  the 


$§94,95]      The  Reception  of  the  Coppernican  Ideas  127 

tables  naturally  had  great  weight  in  inducing  the  astro- 
nomical world  gradually  to  recognise  the  merits  of  the 
Coppernican  system,  at  any  rate  as  a  basis  for  calculating 
the  places  of  the  celestial  bodies. 

Reinhold  was  unfortunately  cut  off  by  the  plague  in 
1553,  and  with  him  disappeared  a  commentary  on  the  De 
Revolutionibus  which  he  had  prepared  but  not  published. 

95.  Very  soon  afterwards  we  find  the  first  signs  that  the 
Coppernican  system  had  spread  into   England.     In    1556 
John  Field  published  an  almanack  for  the  following  year 
avowedly   based    on   Coppernicus    and    Reinhold,   and   a 
passage  in  the  Whetstone  of  Witte  (1557)  by  Robert  Recorde 
(1510-1558),  our  first  writer   on  algebra,  shews  that  the 
author  regarded  the  doctrines  of  Coppernicus  with  favour, 
even  if  he  did  not  believe  in  them  entirely.     A  few  years 
later  Thomas  Digges  (?-i595),  in  his  Alae  sive  Scalae  Mathe- 
maticae  (1573),  an  astronomical  treatise  of  no  great  import- 
ance, gave  warm  praise  to  Coppernicus  and  his  ideas. 

96.  For  nearly  half  a  century  after  the  death  of  Reinhold 
no  important  contributions  were  made  to  the  Coppernican 
controversy.      Reinhold's    tables    were    doubtless    slowly 
doing   their  work  in   familiarising   men's  minds  with    the 
new  ideas,  but  certain  definite  additions  to  knowledge  had 
to  be  made  before  the  evidence  for  them  could  be  regarded 
as  really  conclusive. 

The  serious  mechanical  difficulties  connected  with  the 
Assumption  of  a  rapid  motion  of  the  earth  which  is  quite 
imperceptible  to  its  inhabitants  could  only  be  met  by 
further  progress  in  mechanics,  and  specially  in  knowledge 
of  the  laws  according  to  which  the  motion  of  bodies  is 
produced,  kept  up,  changed,  or  destroyed ;  in  this  direction 
no  considerable  progress  was  made  before  the  time  of 
Galilei,  whose  work  falls  chiefly  into  the  early  i7th  century 
(cf.  chapter  vi.,  §§  116,  130,  133). 

The  objection  to  the  Coppernican  scheme  that  the  stars 
shewed  no  such  apparent  annual  motions  as  the  motion 
of  the  earth  should  produce  (chapter  iv.,  §  92)  would  also 
be  either  answered  or  strengthened  according  as  improved 
methods  of  observation  did  or  did  not  reveal  the  required 
motion. 

Moreover  the  Prussian   Tables,  although  more  accurate 


128  A  Short  History  of  Astronomy  [CH.  v. 

than  the  Alfonsine^  hardly  claimed,  and  certainly  did  not 
possess,  minute  accuracy.  Coppernicus  had  once  told 
Rheticus  that  he  would  be  extravagantly  pleased  if  he 
could  make  his  theory  agree  with  observation  to  within  10' ; 
but  as  a  matter  of  fact  discrepancies  of  a  much  more 
serious  character  were  noticed  from  time  to  time.  The 
comparatively  small  number  of  observations  available  and 
their  roughness  made  it  extremely  difficult,  either  to  find 
the  most  satisfactory  numerical  data  necessary  for  the 
detailed  development  of  any  theory,  or  to  test  the  theory 
properly  by  comparison  of  calculated  with  observed  places 
of  the  celestial  bodies.  Accordingly  it  became  evident  to 
more  than  one  astronomer  that  one  of  the  most  pressing 
needs  of  the  science  was  that  observations  should  be  taken 
on  as  large  a  scale  as  possible  and  with  the  utmost 
attainable  accuracy.  To  meet  this  need  two  schools  of 
observational  astronomy,  of  very  unequal  excellence,  de- 
veloped during  the  latter  half  of  the  i6th  century,  and 
provided  a  mass  of  material  for  the  use  of  the  astronomers 
of  the  next  generation.  Fortunately  too  the  same  period  was 
marked  by  rapid  progress  in  algebra  and  allied  branches  of 
mathematics.  Of  the  three  great  inventions  which  have  so 
enormously  diminished  the  labour  of  numerical  calculations, 
one,  the  so-called  Arabic  notation  (chapter  in.,  §  64), 
was  already  familiar,  the  other  two  (decimal  fractions  and 
logarithms)  were  suggested  in  the  i6th  century  and  were 
in  working  order  early  in  the  iyth  century. 

97.  The  first  important  set  of  observations  taken  after 
the  death  of  Regiomontanus  and  Walther  (chapter  in.,  §  68) 
were  due  to  the  energy  of  the  Landgrave  William  IV.  of 
Hesse  (1532-1592).  He  was  remarkable  as  a  boy  for  his 
love  of  study,  and  is  reported  to  have  had  his  interest  in 
astronomy  created  or  stimulated  when  he  was  little  more 
than  20  by  a  copy  of  Apian's  beautiful  Astronomicum 
Caesareum,  the  cardboard  models  in  which  he  caused  to  be 
imitated  and  developed  in  metal-work.  He  went  on  with 
the  subject  seriously,  and  in  1561  had  an  observatory  built 
at  Cassel,  which  was  remarkable  as  being  the  first  which  had 
a  revolving  roof,  a  device  now  almost  universal.  In  this  he 
made  extensive  observations  (chiefly  of  fixed  stars)  during 
the  next  six  years.  The  death  of  his  father  then  compelled 


H  97, 98]  The  Cassel  Observatory  129 

him  to  devote  most  of  his  energy  to  the  duties  of  govern 
ment,  and  his  astronomical  ardour  abated.  A  few  years 
later,  however  (1575),  as  the  result  of  a  short  visit  from 
the  talented  and  enthusiastic  young  Danish  astronomer 
Tycho  Brahe  (§  99),  he  renewed  his  astronomical  work,  and 
secured  shortly  afterwards  the  services  of  two  extremely  able 
assistants,  Christian  Rothjnann  (in  1577)  a.nd.Joost  Burgi 
(in  1579).  Rothmann,  of  whose  life  extremely  little  is 
known,  appears  to  have  been  a  mathematician  and  theo- 
retical astronomer  of  considerable  ability,  and  was  the 
author  of  several  improvements  in  methods  of  dealing 
with  various  astronomical  problems.  He  was  at  first  a 
Coppernican,  but  shewed  his  independence  by  calling 
attention  to  the  needless  complication  introduced  by 
Coppernicus  in  resolving  the  motion  of  the  earth  into 
three  motions  when  two  sufficed  (chapter  iv.,  §  79).  His 
faith  in  the  system  was,  however,  subsequently  shaken  by 
the  errors  which  observation  revealed  in  the  Prussian  Tables. 
Burgi  (1552-1632)  was  originally  engaged  by  the  Landgrave 
as  a  clockmaker,  but  his  remarkable  mechanical  talents 
were  soon  turned  to  astronomical  account,  and  it  then 
appeared  that  he  also  possessed  unusual  ability  as  a 
mathematician.* 

98.  The  chief  work  of  the  Cassel  Observatory  was  the 
formation  of  a  star  catalogue.  The  positions  of  stars  were 
compared  with  that  of  the  sun,  Venus  or  Jupiter  being 
used  as  connecting  links,  and  their  positions  relatively  to 
the  equator  and  the  first  point  of  Aries  (r)  deduced; 
allowance  was  regularly  made  for  the  errors  due  to  the 
refraction  of  light  by  the  atmosphere,  as  well  as  for  the 
parallax  of  the  sun,  but  the  most  notable  new  departure 
was  the  use  of  a  clock  to  record  the  time  of  observa- 
tions and  to  measure  the  motion  of  the  celestial  sphere. 
The  construction  of  clocks  of  sufficient  accuracy  for  the 
purpose  was  rendered  possible  by  the  mechanical  genius 
of  Burgi,  and  in  particular  by  his  discovery  that  a  clock 
could  be  regulated  by  a  pendulum,  a  discovery  which  he 

There  is  little  doubt  that  he  invented  what  were  substantially 
legarithms  independently  of  Napier,  but,  with  characteristic  inability 
or  unwillingness  to  proclaim  his  discoveries,  allowed  the  invention 
to  die  with  him. 


130  A  Short  History  oj  Astronomy  [CH.  v. 

appears  to  have  taken  no  steps  to  publish,  and  which  had 
in  consequence  to  be  made  again  independently  before  it 
received  general  recognition.*  By  1586  121  stars  had  been 
carefully  observed,  but  a  more  extensive  catalogue  which 
was  to  have  contained  more  than  a  thousand  stars  was 
never  finished,  owing  to  the  unexpected  disappearance  of 
Rothmann  in  15 got  and  the  death  of  the  Landgrave  two 
years  later. 

99.  The  work  of  the  Cassel  Observatory  was,  however, 
overshadowed  by  that  carried  out  nearly  at  the  same  time 
by  Tycho  (Tyge)  Brake.  He  was  born  in  1546  at  Knudstrup 
in  the  Danish  province  of  Scania  (now  the  southern 
extremity  of  Sweden),  being  the  eldest  child  of  a  nobleman 
who  was  afterwards  governor  of  Helsingborg  Castle.  He 
was  adopted  as  an  infant  by  an  uncle,  and  brought  up 
at  his  country  estate.  When  only  13  he  went  to  the 
University  of  Copenhagen,  where  he  began  to  study 
rhetoric  and  philosophy,  with  a  view  to  a  political  career. 
He  was,  however,  very  much  interested  by  a  small  eclipse 
of  the  sun  which  he  saw  in  1560,  and  this  stimulus,  added 
to  some  taste  for  the  astrological  art  of  casting  horoscopes, 
led  him  to  devote  the  greater  part  of  the  remaining  two 
years  spent  at  Copenhagen  to  mathematics  and  astronomy. 
In  1562  he  went  on  to  the  University  of  Leipzig,  accom- 
panied, according  to  the  custom  of  the  time,  by  a  tutor, 
who  appears  to  have  made  persevering  but  unsuccessful 
attempts  to  induce  his  pupil  to  devote  himself  to  law. 
Tycho,  however,  was  now  as  always  a  difficult  person  to  divert 
from  his  purpose,  and  went  on  steadily  with  his  astronomy. 
In  1563  he  made  his  first  recorded  observation,  of  a  close 
approach  of  Jupiter  and  Saturn,  the  time  of  which  he  noticed 
to  be  predicted  a  whole  month  wrong  by  the  Alfonsine 
Tables  (chapter  in.,  §  66),  while  the  Prussian  Tables  (§  94) 
were  several  days  in  error.  While  at  Leipzig  he  bought 
also  a  few  rough  instruments,  and  anticipated  one  of  the 
great  improvements  afterwards  carried  out  systematically, 

*  A  similar  discovery  was  in  fact  made  twice  again,  by  Galilei 
(chapter  vi.,  §  114)  and  by  Huygens  (chapter  vin.,  §  157). 

f  He  obtained  leave  of  absence  to  pay  a  visit  to  Tycho  Brahe 
and  never  returned  to  Cassel.  He  must  have  died  between  \yq 
and  1608. 


M  9:,  xoj]  Early  Life  of  Tycho  Brake  131 

by  trying  to  estimate  and  to  allow  for  the  errors  of  his 
instruments. 

In  1565  Tycho  returned  to  Copenhagen,  probably  on 
account  of  the  war  with  Sweden  which  had  just  broken  out, 
and  stayed  about  a  year,  during  the  course  of  which  he  lost 
his  uncle.  He  then  set  out  again  (1566)  on  his  travels, 
and  visited  Wittenberg,  Rostock,  Basle,  Ingolstadt,  Augsburg, 
and  other  centres  of  learning,  thus  making  acquaintance 
with  several  of  the  most  notable  astronomers  of  Germany. 
At  Augsburg  he  met  the  brothers  Hainzel,  rich  citizens 
with  a  taste  for  science,  for  one  of  whom  he  designed  and 
had  constructed  an  enormous  quadrant  (quarter-circle) 
with  a  radius  of  about  19  feet,  the  rim  of  which  was 
graduated  to  single  minutes  ;  and  he  began  also  here  the 
construction  of  his  great  celestial  globe,  five  feet  in  diameter, 
on  which  he  marked  one  by  one  the  positions  of  the  stars 
as  he  afterwards  observed  them. 

In  1570  Tycho  returned  to  his  father  at  Helsingborg, 
and  soon  after  the  death  of  the  latter  (1571)  went  for 
a  long  visit  to  Steen  Bille,  an  uncle  with  scientific  tastes. 
During  this  visit  he  seems  to  have  devoted  most  of  his 
time  to  chemistry  (or  perhaps  rather  to  alchemy),  and  his 
astronomical  studies  fell  into  abeyance  for  a  time. 

100.  His  interest  in  astronomy  was  fortunately  revived 
by  the  sudden  appearance,  in  November  1572,  of  a  brilliant 
new  star  in  the  constellation  Cassiopeia.  Of  this  Tycho 
took  a  number  of  extremely  careful  observations ;  he  noted 
the  gradual  changes  in  its  brilliancy  from  its  first  appearance, 
when  it  rivalled  Venus  at  her  brightest,  down  to  its  final 
disappearance  16  months  later.  He  repeatedly  measured 
its  angular  distance  from  the  chief  stars  in  Cassiopeia, 
and  applied  a  variety  of  methods  to  ascertain  whether  ic 
had  any  perceptible  parallax  (chapter  n.,  §§  43,  49).  Nu 
parallax  could  be  definitely  detected,  and  he  deduced  accord 
ingly  that  the  star  must  certainly  be  farther  off  than  the  moon  ; 
as  moreover  it  had  no  share  in  the  planetary  motions,  he 
inferred  that  it  must  belong  to  the  region  of  the  fixed  stars. 
To  us  of  to-day  this  result  may  appear  fairly  commonplace, 
but  most  astronomers  of  the  time  held  so  firmly  to  Aristotle's 
doctrine  that  the  heavens  generally,  and  the  region  of  the 
fixed  stars  in  particular,  were  incorruptible  and  unchange- 


132  A  Short  History  of  Astronomy       [CH.  V.,  $101 

able,  that  new  stars  were,  like  comets,  almost  universally 
ascribed  to  the  higher  regions  of  our  own  atmosphere. 
Tycho  wrote  an  account  of  the  new  star,  which  he  was  ulti- 
mately induced  by  his  friends  to  publish  (1573),  together 
with  some  portions  of  a  calendar  for  that  year  which  he  had 
prepared.  His  reluctance  to  publish  appears  to  have  been 
due  in  great  part  to  a  belief  that  it  was  unworthy  of  the 
dignity  of  a  Danish  nobleman  to  write  books !  The 
book  in  question  (De  Nova  .  .  .  Stella)  compares  very 
favourably  with  the  numerous  other  writings  which  the 
star  called  forth,  though  it  shews  that  Tycho  held  the 
common  beliefs  that  comets  were  in  our  atmosphere,  and 
that  the  planets  were  carried  round  by  solid  crystalline 
spheres,  two  delusions  which  his  subsequent  work  did 
much  to  destroy.  He  also  dealt  at  some  length  with  the 
astrological  importance  of  the  star,  and  the  great  events 
which  it  foreshadowed,  utterances  on  which  Kepler  sub- 
sequently made  the  very  sensible  criticism  that  "if  that 
star  did  nothing  else,  at  least  it  announced  and  produced 
a  great  astronomer.'3 

In  1574  Tycho  was  requested  to  give  some  astronomical 
lectures  at  the  University  of  Copenhagen,  the  first  of  which, 
dealing  largely  with  astrology,  was  printed  in  1610,  after  his 
death.  When  these  were  finished,  he  set  off  again  on  his 
travels  (1575).  After  a  short  visit  to  Cassel  (§  97),  during 
which  he  laid  the  foundation  of  a  lifelong  friendship  with 
the  Landgiave,  he  went  on  to  Frankfort  to  buy  books, 
thence  to  Basle  (where  he  had  serious  thoughts  of  settling) 
and  on  to  Venice,  then  back  to  Augsburg  and  to  Regens- 
burg,  where  he  obtained  a  copy  of  the  Commentariolus  of 
Coppernicus  (chapter  iv.,  §  73),  and  finally  came  home 
by  way  of  Saalfeld  and  Wittenberg. 

1 01.  The  next  year  (1576)  was  the  beginning  of  a 
.new  epoch  in  Tycho's  career.  The  King  of  Denmark, 
Frederick  II.,  who  was  a  zealous  patron  of  science  and 
literature,  determined  to  provide  Tycho  with  endowments 
sufficient  to  enable  him  to  carry  out  his  astronomical  work 
in  the  most  effective  way.  He  accordingly  gave  him  for 
occupation  the  little  island  of  Hveen  in  the  Sound  (now 
belonging  to  Sweden),  promised  money  for  building  a 
house  and  observatory,  and  supplemented  the  income 


134  A  Short  History  of  Astronomy  [Cn.  v. 

derived  from  the  rents  of  the  island  by  an  annual  payment 
cf  about  ;£ioo.  Tycho  paid  his  first  visit  to  the  island  in 
May,  soon  set  to  work  building,  and  had  already  begun  to 
make  regular  observations  in  his  new  house  before  the 
end  of  the  year. 

The  buildings  were  as  remarkable  for  their  magnificence 
as  for  their  scientific  utility.  Tycho  never  forgot  that  he  was 
a  Danish  nobleman  as  well  as  an  astronomer,  and  built  in 
a  manner  suitable  to  his  rank.*  His  chief  building  (fig.  51), 
called  Uraniborg  (the  Castle  of  the  Heavens),  was  in  the 
middle  of  a  large  square  enclosure,  laid  out  as  a  garden, 
the  corners  of  which  pointed  North,  East,  South,  and  West, 
and  contained  several  observatories,  a  library  and  laboratory, 
in  addition  to  living  rooms.  Subsequently,  when  the  number 
of  pupils  and  assistants  who  came  to  him  had  increased, 
he  erected  (1584)  a  second  building,  Stjerneborg  (Star 
Castle),  which  'was  remarkable  for  having  underground 
observatories.  The  convenience  of  being  able  to  carry  out 
all  necessary  work  on  his  own  premises  induced  him 
moreover  to  establish  workshops,  where  nearly  all  his 
instruments  were  made,  and  afterwards  also  a  printing  press 
and  paper  mill.  Both  at  Uraniborg  and  Stjerneborg  not 
only  the  rooms,  but  even  the  instruments  which  were 
gradually  constructed,  were  elaborately  painted  or  otherwise 
ornamented. 

102.  The  expenses  of  the  establishment  must  have  been 
enormous,  particularly  as  Tycho  lived  in  magnificent  style 
and  probably  paid  little  attention  to  economy.  His  income 
was  derived  from  various  sources,  and  fluctuated  from  time 
to  time,  as  the  King  did  not  merely  make  him  a  fixed 
annual  payment,  but  added  also  temporary  grants  of  lands 
or  money.  Amongst  other  benefactions  he  received  in 
1579  one  of  the  canonries  of  the  cathedral  of  Roskilde, 
the  endowments  of  which  had  been  practically  secularised 
at  the  Reformation.  Unfortunately  most  of  his  property 
was  held  on  tenures  which  involved  corresponding  obliga- 
tions, and  as  he  combined  the  irritability  of  a  genius 
with  the  haughtiness  of  a  mediaeval  nobleman,  continual 
quarrels  were  the  result.  Very  soon  after  his  arrival  at 

*  He  even  did  not  forget  to  provide  one  of  the  most  necessary 
parts  of  a  mediaeval  castle,  a  prison  ! 


$$  io2,  IDS]  Life  at  Hveen  135 

Hveen  his  tenants  complained  of  work  which  he  illegally 
fi.Tced  from  them;  chapel  services  which  his  canonry 
required  him  to  keep  up  were  neglected,  and  he  entirely 
refused  to  make  certain  recognised  payments  to  the  widow 
of  the  previous  canon.  Further  difficulties  arose  out  of  a 
lighthouse,  the  maintenance  of  which  was  a  duty  attached 
to  one  of  his  estates,  but  was  regularly  neglected.  Nothing 
shews  the  King's  good  feeling  towards  Tycho  more  than 
the  trouble  which  he  took  to  settle  these  quarrels,  often 
ending  by  paying  the  sum  of  money  under  dispute.  Tycho 
was  moreover  extremely  jealous  of  his  scientific  reputation, 
and  on  more  than  one  occasion  broke  out  into  violent 
abuse  of  some  assistant  or  visitor  whom  he  accused  of 
stealing  his  ideas  and  publishing  them  elsewhere. 

In  addition  to  the  time  thus  spent  in  quarrelling,  a  good 
deal  must  have  been  occupied  in  entertaining  the  numerous 
visitors  whom  his  fame  attracted,  and  who  included,  in 
addition  to  astronomers,  persons  of  rank  such  as  several 
of  the  Danish  royal  family  and  James  VI.  of  Scotland 
(afterwards  James  I.  of  England). 

Notwithstanding  these  distractions,  astronomical  work 
made  steady  progress,  and  during  the  21  years  that  Tycho 
spent  at  Hveen  he  accumulated,  with  the  help  of  pupils 
and  assistants,  a  magnificent  series  of  observations,  far 
transcending  in  accuracy  and  extent  anything  that  had 
been  accomplished  by  his  predecessors.  A  good  deal  of 
attention  was  also  given  to  alchemy,  and  some  to  medicine. 
He  seems  to  have  been  much  impressed  with  the  idea 
of  the  unity  of  Nature,  and  to  have  been  continually 
looking  out  for  analogies  or  actual  connection  between 
the  different  subjects  which  he  studied. 

103.  In  1577  appeared  a  brilliant  comet,  which  Tycho 
observed  with  his  customary  care;  and,  although  he  had 
not  at  the  time  his  full  complement  of  instruments,  his 
observations  were  exact  enough  to  satisfy  him  that  the 
comet  was  at  least  three  times  as  far  off  as  the  moon,  and 
thus  to  refute  the  popular  belief,  which  he  had  himself 
held  a  few  years  before  (§  100),  that  comets  were  generated 
in  our  atmosphere.  His  observations  led  him  also  to  the 
belief  that  the  comet  was  revolving  round  the  sun,  at  a 
distance  from  it  greater  than  that  of  Venus,  a  conclusion 


136  A  Short  History  of  Astronomy  [Cn.  v. 

I  which  interfered  seriously  with  the  common  doctrine  of 
the  solid  crystalline  spheres.  He  had  further  opportunities 
of  observing  comets  in  1580,  1582,  1585,  1590,  and  1596, 
and  one  of  his  pupils  also  took  observations  of  a  comet 
seen  in  1593.  None  of  these  comets  attracted  as  much 
general  attention  as  that  of  1577,  but  Tycho's  observations, 
as  was  natural,  gradually  improved  in  accuracy. 

104.  The  valuable  results  obtained  by  means  of  the  new 
star  of  1572,  and  by  the  comets,  suggested  the  propriety  of 
undertaking  a  complete  treatise  on  astronomy  embodying 
these  and   other  discoveries.      According  to  the   original 
plan,  there  were  to  be  three  preliminary  volumes  devoted 
respectively  to  the  new  star,  to  the  comet  of  1577,  and  to 
the  later  comets,  while  the  main  treatise  was  to  consist  of 
several  more  volumes  dealing  with  the  theories  of  the  sun, 
moon,  and  planets.     Of  this  magnificent  plan  comparatively 
little   was   ever  executed.      The   first   volume,   called   the 
Astronomiae   Instauratae  Progymnasmata,  or  Introduction 
to  the  New  Astronomy,  was  hardly  begun  till  1588,  and, 
although  mostly  printed  by  1592,  was  never  quite  finished 
during  Tycho's    lifetime,    and   was   actually   published   by 
Kepler  in    1602.      One   question,  in  fact,  led  to  another 
in    such    a  way  that   Tycho  felt   himself  unable   to   give 
a     satisfactory    account     of    the    star    of     1572     without 
dealirg  with  a  number  of  preliminary  topics,  such  as  the 
positions   of  the  fixed   stars,    precession,    and  the  annual 
motion     of    the     sun,     each    of    which    necessitated    an 
elaborate  investigation.     The  second  volume,  dealing  with 
the  comet  of  1577,  called  De  Mundi  aether ei  recentioribus 
Phaenomenis   Liber  secundus  (Second    book   about   recent 
appearances    in    the  Celestial    World),    was   finished   long 
before    the   first,    and    copies   were   sent   to    friends   and 
correspondents  in   1588,  though  it  was  not  regularly  pub- 
lished and  on  sale  till  1603.     The  third  volume  was  never 
written,  though  some  material  was  collected  for  it,  and  the 
main  treatise  does  not  appear  to  have  been  touched. 

105.  The   book   on   the   comet   of   1577    is    of  special 
interest,  as  containing  an  account  of  Tycho's  system  of  the 
world,  which  was  a  compromise  between  those  of  Ptolemy 
and  of  Coppernicus.     Tycho  was  too  good  an  astronomer 
not    to   realise    many   of    the    simplifications    which    the 


io4,  IDS]  Tychtfs  System  of  the    World 


137 


Coppernican  system  introduced,  but  was  unable  to  answer 
two  of  the  serious  objections  ;  he  regarded  any  motion  of 


FIG.  52. — Tycho's  system  of  the  world.     From  his  book  on  the 
comet  of  1577. 

"  the  sluggish  and  heavy  earth "  as  contrary  to  "  physical 
principles,"  and  he  objected  to  the  great  distance  of  the 


138  A  Short  History  of  Astronomy  [CH  v. 

stars  which  the  Coppernican  system  required,  because  a  vast 
empty  space  would  be  left  between  them  and  the  planets, 
a  space  which  he  regarded  as  wasteful.*  Biblical  difficul- 
ties t  also  had  some  weight  with  him.  He  accordingly 
devised  (1583)  a  new  system  according  to  which  the  five 
planets  revolved  round  the  sun  (c,  in  fig.  52),  while  the  sun 
revolved  annually  round  the  earth  (A),  and  the  whole  celestial 
sphere  performed  also  a  daily  revolution  round  the  earth. 
The  system  was  never  worked  out  in  detail,  and,  like  many 
compromises,  met  with  little  support;  Tycho  nevertheless 
was  extremely  proud  of  it,  and  one  of  the  most  violent  and 
prolonged  quarrels  of  his  life  (lasting  a  dozen  years)  was  with 
Reymers  Bar  or  Ursus  (?-i6oo),  who  had  communicated 
to  the  Landgrave  in  1586  and  published  two  years  later  a 
system  of  the  world  very  like  Tycho's.  Reymers  had  been 
at  Hveen  for  a  short  time  in  1584,  and  Tycho  had  no  hesita- 
tion in  accusing  him  of  having  stolen  the  idea  from  some 
manuscript  seen  there.  Reymers  naturally  retaliated  with 
a  counter-charge  of  theft  against  Tycho.  There  is,  how- 
ever, no  good  reason  why  the  idea  should  not  have  occurred 
independently  to  each  astronomer;  and  Reymers  made  in 
some  respects  a  great  improvement  on  Tycho's  scheme  by 
accepting  the  daily  rotation  of  the  earth,  and  so  doing 
away  with  the  daily  rotation  of  the  celestial  sphere,  which 
was  certainly  one  of  the  weakest  parts  of  the  Ptolemaic 
scheme. 

1 06.  The  same  year  (1588)  which  saw  the  publication  of 
Tycho's  book  on  the  comet  was  also  marked  by  the  death 
of  his  patron,  Frederick  II.  The  new  King  Christian  was 
a  boy  of  n,  and  for  some  years  the  country  was  managed 
by  four  leading  statesmen.  The  new  government  seems  to 
have  been  at  first  quite  friendly  to  Tycho  ;  a  large  sum  was 
paid  to  him  for  expenses  incurred  at  Hveen,  and  additional 
endowments  were  promised,  but  as  time  went  on  Tycho's 
usual  quarrels  with  his  tenants  and  others  began  to  produce 

*  It  would  be  interesting  to  know  what  use  he  assigned  to  the 
(presumably)  still  vaster  space  beyond  the  stars. 

•j-  Tycho  makes  in  this  connection  the  delightful  remark  that 
Moses  must  have  been  a  skilled  astronomer,  because  he  refers  to 
the  moon  as  "the  lesser  light,"  notwithstanding  the  fact  thot  the 
apparent  diameters  of  sun  and  moon  are  very  nearly  equal  ! 


TYCHO    BRAHE. 


[To  face  p.  139. 


$$  io6,   i  7]  Last   Years  at  Hveen  139 

their  effect.  In  1594  he  lost  one  of  his  chief  supporters 
at  court,  the  Chancellor  Kaas,  and  his  successor,  as  well  as 
two  or  three  other  important  officials  at  court,  were  not 
very  friendly,  although  the  stories  commonly  told  of  violent 
personal  animosities  appear  to  have  little  foundation.  As 
early  as  1591  Tycho  had  hinted  to  a  correspondent  that 
he  might  not  remain  permanently  in  Denmark,  and  in  1594 
he  began  a  correspondence  with  representatives  of  the 
Emperor  Rudolph  II.,  who  was  a  patron  of  science.  But 
his  scientific  activity  during  these  years  was  as  great  as 
ever;  and  in  1596  he  completed  the  printing  of  an 
extremely  interesting  volume  of  scientific  correspondence 
between  the  Landgrave,  Rothmann,  and  himself.  The 
accession  of  the  young  King  to  power  in  1596  was  at  once 
followed  by  the  withdrawal  of  one  of  Tycho's  estates,  and 
in  the  following  year  the  annual  payment  which  had  been 
made  since  1576  was  stopped.  It  is  difficult  to  blame  the 
King  for  these  economies  ;  he  was  evidently  not  as  much 
interested  in  astronomy  as  his  father,  and  consequently  re- 
garded the  heavy  expenditure  at  Hveen  as  an  extravagance, 
and  it  is  also  probable  that  he  was  seriously  annoyed  at 
Tycho's  maltreatment  of  his  tenants,  and  at  other  pieces  of 
unruly  conduct  on  his  part.  Tycho,  however,  regarded  the 
forfeiture  of  his  annual  pension  as  the  last  straw,  and  left 
Hveen  early  in  1597,  taking  his  more  portable  property 
with  him.  After  a  few  months  spent  in  Copenhagen,  he 
took  the  decisive  step  of  leaving  Denmark  for  Germany, 
in  return  for  which  action  the  King  deprived  him  of  his 
canonry.  Tycho  thereupon  wrote  a  remonstrance  in 
which  he  pointed  out  the  impossibility  of  carrying  on  his 
work  without  proper  endowments,  and  offered  to  return 
if  his  services  were  properly  appreciated.  The  King, 
however,  was  by  this  time  seriously  annoyed,  and  his  reply 
was  an  enumeration  of  the  various  causes  of  complaint 
against  Tycho  which  had  arisen  of  late  years.  Although 
Tycho  made  some  more  attempts  through  various  friends 
to  regain  royal  favour,  the  breach  remained  final. 

107.  Tycho  spent  the  winter  1597-8  with  a  friend  near 
Hamburg,  and,  while  there,  issued,  under  the  title  of 
Astronomiae  Instauratae  Mechanica,  a  description  of  his 
instruments,  together  with  a  short  autobiography  and  an 


140  A  Short  History  of  Astronomy  [Cn.  v. 

interesting  account  of  his  chief  discoveries.  About  the 
same  time  he  circulated  manuscript  copies  of  a  catalogue 
of  1,000  fixed  stars,  of  which  only  777  had  been  properly, 
observed,  the  rest  having  been  added  hurriedly  to  make 
up  the  traditional  number.  The  catalogue  and  the 
Mechanica  were  both  intended  largely  as  evidence  of  his 
astronomical  eminence,  and  were  sent  to  various  influential 
persons.  Negotiations  went  on  both  with  the  Emperor 
and  with  the  Prince  of  Orange,  and  after  another  year  spent 
in  various  parts  of  Germany,  Tycho  definitely  accepted  an 
invitation  of  the  Emperor  and  arrived  at  Prague  in  June 

J599- 

1 08.  It  was  soon  agreed  that  he  should  inhabit  the 
castle  of  Benatek,  some  twenty  miles  from  Prague,  where  he 
accordingly  settled  with  his  family  and  smaller  instruments 
towards  the  end  of  1599.  He  at  once  started  observing, 
sent  one  of  his  sons  to  Hveen  for  his  larger  instruments, 
and  began  looking  about  for  assistants.  He  secured  one  of 
the  most  able  of  his  old  assistants,  and  by  good  fortune 
was  also  able  to  attract  a  far  greater  man,  John  Kepler ;  to 
whose  skilful  use  of  the  materials  collected  by  Tycho  the 
latter  owes  no  inconsiderable  part  of  his  great  reputation. 
Kepler,  whose  life  and  work  will  be  dealt  with  at 
length  in  chapter  vii.,  had  recently  published  his  first 
important  work,  the  Mysterium  Cosmographicum  (§  136), 
which  had  attracted  the  attention  of  Tycho  among  others, 
and  was  beginning  to  find  his  position  at  Gratz  in  Styria 
uncomfortable  on  account  of  impending  religious  disputes. 
After  some  hesitation  he  joined  Tycho  at  Benatek  early 
in  1600.  He  was  soon  set  to  work  at  the  study  of  Mars 
for  the  planetary  tables  which  Tycho  was  then  preparing, 
and  thus  acquired  special  familiarity  with  the  observations 
of  this  planet  which  Tycho  had  accumulated.  The  re- 
lations of  the  two  astronomers  were  not  altogether  happy, 
Kepler  being  then  as  always  anxious  about  money  matters, 
and  the  disturbed  state  of  the  country  rendering  it 
difficult  for  Tycho  to  get  payment  from  the  Emperor. 
Consequently  Kepler  very  soon  left  Benatek  and  returned 
to  Prague,  where  he  definitely  settled  after  a  short  visit 
to  Gratz;  Tycho  also  moved  there  towards  the  end  of 
1600,  and  they  then  worked  together  harmoniously  for 


$$  IDS— no]  Tycho's  Last   Years  141 

the  short  remainder  of  Tycho's  life.  Though  he  -was 
by  no  means  an  old  man,  there  were  some  indications 
that  his  health  was  failing,  and  towards  the  end  of  1601 
he  was  suddenly  seized  with  an  illness  which  terminated 
fatally  after  a  few  days  (November  24th).  It  is  charac- 
teristic of  his  devotion  to  the  great  work  of  his  life  that 
in  the  delirium  which  preceded  his  death  he  cried  out 
again  and  again  his  hope  that  his  life  might  not  prove  to 
have  been  fruitless  (Nefrustra  vixisse  videar). 

109.  Partly  owing  to  difficulties  between  Kepler  and 
one  of  Tycho's  family,  partly  owing  to  growing  political 
disturbances,  scarcely  any  use  was  made  of  Tycho's  instru- 
ments after  his  death,  and  most  of  them  perished  during 
the  Civil  Wars  in  Bohemia.  Kepler  obtained  possession 
of  his  observations  ;  but  they  have  never  been  published 
except  in  an  imperfect  form. 

no.  Anything  like  a  satisfactory  account  of  Tycho's 
services  to  astronomy  would  necessarily  deal  largely  with 
technical  details  of  methods  of  observing,  which  would 
be  out  of  place  here.  It  may,  however,  be  worth  while 
to  attempt  to  give  some  general  account  of  his  charac- 
teristics as  an  observer  before  referring  to  special  dis- 
coveries. 

Tycho  realised  more  fully  than  any  of  his  predecessors 
the  importance  of  obtaining  observations  which  should  not 
only  be  as  accurate  as  possible,  but  should  be  taken  so 
often  as  to  preserve  an  almost  continuous  record  of  the 
positions  and  motions  of  the  celestial  bodies  dealt  with  ; 
whereas  the  prevailing  custom  (as  illustrated  for  example 
by  Coppernicus)  was  only  to  take  observations  now  and 
then,  either  when  an  astronomical  event  of  special  interest 
such  as  an  eclipse  or  a  conjunction  was  occurring,  or  to 
supply  some  particular  datum  required  for  a  point  of  theory. 
While  Coppernicus,  as  has  been  already  noticed  (chapter  iv., 
§  73),  only  used  altogether  a  few  dozen  observations  in 
his  book,  Tycho — to  take  one  instance — observed  the  sun 
daily  for  many  years,  and  must  therefore  have  taken  some 
thousands  of  observations  of  this  one  body,  in  addition  to  the 
many  thousands  which  he  took  of  other  celestial  bodies. 
It  is  true  that  the  Arabs  had  some  idea  of  observing  con- 
tinuously (cf.  chapter  HI.,  §  57),  but  they  had  too  little 


142  A  Short  History  of  Astronomy  [CH.  v. 

speculative  power  or  originality  to  be  able  to  make  much  use 
of  their  observations,  few  of  which  passed  into  the  hands  of 
European  astronomers.  Regiomontanus  (chapter  HI.,  §  68), 
if  he  had  lived,  might  probably  have  to  a  consider- 
able extent  anticipated  Tycho,  but  his  short  life  was 
too  fully  occupied  with  the  study  and  interpretation  of 
Greek  astronomy  for  him  to  accomplish  very  much  in 
other  departments  of  the  subject.  The  Landgrave  and  his 
staff,  who  were  in  constant  communication  with  Tycho, 
were  working  in  the  same  direction,  though  on  the  whole 
less  effectively.  Unlike  the  Arabs,  Tycho  was,  however, 
fully  impressed  with  the  idea  that  observations  were  only 
a  means  to  an  end,  and  that  mere  observations  without 
a  hypothesis  or  theory  to  connect  and  interpret  them  were 
of  little  use. 

The  actual  accuracy  obtained  by  Tycho  in  his  observa- 
tions naturally  varied  considerably  according  to  the  nature 
of  the  observation,  the  care  taken,  and  the  period  of  his 
career  at  which  it  was  made.  The  places  which  he  assigned 
to  nine  stars  which  were  fundamental  in  his  star  catalogue 
differ  from  their  positions  as  deduced  from  the  best  modern 
observations  by  angles  which  are  in  most  cases  less  than  i', 
and  in  only  one  case  as  great  as  2'  (this  error  being  chiefly 
due  to  refraction  (chapter  n.,  §  46),  Tycho's  knowledge  of 
which  was  necessarily  imperfect).  Other  star  places  were 
presumably  less  accurate,  but  it  will  not  be  far  from  the  truth 
if  we  assume  that  in  most  cases  the  errors  in  Tycho's  obser- 
vations did  not  exceed  i'  or  2'.  Kepler  in  a  famous  passage 
speaks  of  an  error  of  8'  in  a  planetary  observation  by 
Tycho  as  impossible.  This  great  increase  in  accuracy  can 
only  be  assigned  in  part  to  the  size  and  careful  construction 
of  the  instruments  used,  the  characteristics  on  which  the 
Arabs  and  other  observers  had  laid  such  stress.  Tycho 
certainly  used  good  instruments,  but  added  very  much  to 
their  efficiency,  partly  by  minor  mechanical  devices,  such  as 
the  use  of  specially  constructed  "  sights  "  and  of  a  particular 
[method  of  graduation,*  and  partly  by  using  instruments 
{capable  only  of  restricted  motions,  and  therefore  of  much 
f  greater  steadiness  than  instruments  which  were  able  to  point 
''  to  any  part  of  the  sky.  Another  extremely  important  idea 
*  By  transversals. 


$  in]  Estimate  of  TyMs    Work  143 

was  that  of  systematically  allowing  as  far  as  possible  for] 
the  inevitable  mechanical  imperfections   of  even  the  best  [ 
constructed  instruments,  as  well   as  for   other  permanent  \ 
causes  of  error.     It  had  been  long  known,   for  example, 
that  the   refraction  of  light  through   the   atmosphere  had 
the   effect  of  slightly  raising  the  apparent  places  of  stars 
in  the  sky.     Tycho  took  a  series  of  observations  to  ascer- 
tain the  amount  of  this  displacement  for  different  parts  of 
the  sky,  hence  constructed  a  table   of  refractions  (a  very 
imperfect  one,  it  is  true),  and  in  future  observations  regularly 
allowed  for  the  effect  of  refraction.     Again,  it  was  known 
that  observations  of  the  sun  and  planets  were  liable  to  be 
disturbed  by  the  effect  of  parallax  (chapter  n.,  §§  43,  49), 
though  the  amount  of  this  correction  was  uncertain.     In 
cases  where   special  accuracy  was  required,  Tycho  accord-    j 
ingly  observed  the  body  in  question  at  least  twice,  choosing    1 
positions  in  which  parallax  was  known  to  produce  nearly   I 
opposite  effects,  and  thus  by  combining   the  observations  f 
obtained  a  result  nearly  free  from  this  particular  source  of 
error.     He    was   also  one    of  the  first  to  realise  fully  the 
importance  of  repeating  the  same  observation  many  times 
under  different  conditions,  in  order  that  the  various  acci- 
dental sources  of  error  in  the  separate  observations  should 
as  far  as  possible  neutralise  one  another. 

in.  Almost  every  astronomical  quantity  of  importance  I 
was  re-determined  and  generally  corrected  by  him.     The  ' 
annual  motion  of  the  sun's  apogee  relative  to  r ,  for  example, 
which  Coppernicus  had  estimated  at  24",  Tycho  fixed  «t 
45",  the  modern  value  being  61";  the  length  of  the  year 
he  determined  with  an  error  of  less  than  a  second ;  and  he 
constructed  tables  of  the  motion  of  the  sun  which  gave  its 
place  to  within  i',  previous  tables  being  occasionally  15'  or 
20'  wrong.    By  an  unfortunate  omission  he  made  no  inquiry  j 
into  the  distance  of  the  sun,  but  accepted  the  extremely  j 
inaccurate  value   which  had   been  handed   down,  without  i 
substantial  alteration,  from  astronomer  to  astronomer  since 
the  time  of  Hipparchus  (chapter  n.,  §  41). 

In  the  theory  of  the  moon  Tycho  made  several  important 
discoveries.  He  found  that  the  irregularities  in  its  move- 
ment were  not  fully  represented  by  the  equation  of  the 
centre  and  the  evection  (chapter  n.,  §§  39,  48),  but  that 


144  A  Short  History  of  Astronomy       [CH.  v.,§n2 

(there  was  a  further  irregularity  which  vanished  at  opposition 
and  conjunction  as  well  as  at  quadratures,  but  in  inter- 
mediate positions  of  the  moon  might  be  as  great  as  40'. 
This  irregularity,  known  as  the  variation,  was,  as  has  been 
already  mentioned  (chapter  in.,  §  60),  very  possibly  dis- 
covered by  Abul  Wafa,  though  it  had  been  entirely  lost 
subsequently.  At  a  later  stage  in  his  career,  at  latest 
during  his  visit  to  Wittenberg  in  1598-9,  Tycho  found  that 
it  was  necessary  to  introduce  a  further  small  inequality 
1  known  as  the  annual  equation,  which  depended  on  the 
I  position  of  the  earth  in  its  path  round  the  sun  ;  this,  how- 
ever, he  never  completely  investigated.  He  also  ascertained 
that  the  inclination  of  the  moon's  orbit  to  the  ecliptic  was 
not,  as  had  been  thought,  fixed,  but  oscillated  regularly, 
and  that  the  motion  of  the  moon's  nodes  (chapter  IL,  §  40) 
was  also  variable. 

112.  Reference   has    already    been    made    to   the   star 

catalogue.     Its  construction  led  to  a  study  of  precession, 

the  amount  of  which  was  determined   with   considerable 

(accuracy;  the  same  investigation  led  Tycho  to  reject  the 

I  supposed  irregularity  in  precession  which,  under  the  name 

of  trepidation  (chapter  in.,  §  58),  had  confused  astronomy 

for  several  centuries,  but  from  this  time  forward  rapidly  lost 

its  popularity. 

The  planets  were  always  a  favourite  subject   of  study 

'  with  Tycho,  but  although  he  made  a  magnificent  series  of 

observations,  of  immense  value  to  his  successors,  he  died 

before  he  could  construct  any  satisfactory  theory  of  the 

planetary  motions.     He  easily  discovered,  however,  that  their 

/  motions  deviated  considerably  from  those  assigned  by  any 

j  of  the  planetary  tables,  and  got  as  far  as  detecting  some 

\  regularity  in  these  deviations. 


CHAPTER   VI. 

GALILEI. 

"Dans  la  Science  nous  sommes  tous  disciples  de  Galilee." — 
TROUESSART. 

"  Bacon  pointed  out  at  a  distance  the  road  to  true  philosophy : 
Galileo  both  pointed  it  out  to  others,  and  made  himself  considerable 
advances  in  it." — DAVID  HUME. 

113.  To  the  generation  which  succeeded  Tycho  belonged 
two  of  the  best  known  of  all  astronomers,  Galilei  and  Kepler. 
Although  they  were  nearly  contemporaries,  Galilei  having 
been  born  seven  years  earlier  than  Kepler,  and  surviving 
him  by  twelve  years,  their  methods  of  work  and  their 
contributions  to  astronomy  were  so  different  in  character, 
and  their  influence  on  one  another  so  slight,  that  it  is 
convenient  to  make  some  departure  from  strict  chrono- 
logical order,  and  to  devote  this  chapter  exclusively  to 
Galilei,  leaving  Kepler  to  the  next. 

Galileo  Galilei  was  born  in  1564,  at  Pisa,  at  that  time 
in  the  Grand  Duchy  of  Tuscany,  on  the  day  of  Michel 
Angelo's  death  and  in  the  year  of  Shakespeare's  birth. 
His  father,  Vincenzo,  was  an  impoverished  member  of  a 
good  Florentine  family,  and  was  distinguished  by  his  skill 
in  music  and  mathematics.  Galileo's  talents  shewed  them- 
selves early,  and  although  it  was  originally  intended  that 
he  should  earn  his  living  by  trade,  Vincenzo  was  wise 
enough  to  see  that  his  son's  ability  and  tastes  rendered  him 
much  more  fit  for  a  professional  career,  and  accordingly 
he  sent  him  in  1581  to  study  medicine  at  the  University 
of  Pisa.  Here  his  unusual  gifts  soon  made  him  con- 
spicuous, and  he  became  noted  in  particular  for  his 
unwillingness  to  accept  without  question  the  dogmatic 
statements  of  his  teachers,  which  were  based  not  on  direct 

"*  10 


146  A  Short  History  oj  Astronomy  [CH.  vi. 

evidence,  but  on  the  authority  of  the  great  writers  of  the 
past.  This  valuable  characteristic,  which  marked  him 
throughout'  his  life,  coupled  with  his  skill  in  argument, 
earned  for  him  the  dislike  of  some  of  his  professors,  and 
from  his  fellow-students  the  nickname  of  The  Wrangler. 

114.  In  1582  his  keen  observation  led  to  his  first  scien- 
tific discovery.     Happening  one  day  in  the  Cathedral  of 
Pisa  to  be  looking  at  the  swinging  of  a  lamp  which  was 
hanging    from   the   roof,  he    noticed   that   as    the    motion 
gradually   died    away   and   the    extent   of  each  oscillation 

\became  less,  the  time  occupied  by  each  oscillation  remained 
Jsensibly  the  same,  a  result  which  he  verified  more  precisely 
by  comparison  with  the  beating  of  his  pulse.  Further 
thought  and  trial  shewed  him  that  this  property  was  not 
peculiar  to  cathedral  lamps,  but  that  any  weight  hung  by 
a  string  (or  any  other  form  of  pendulum)  swung  to  and  fro 
in  a  time  which  depended  only  on  the  length  of  the  string 
and  other  characteristics  of  the  pendulum  itself,  and  not 
to  any  appreciable  extent  on  the  way  in  which  it  was  set 
in  motion  or  on  the  extent  of  each  oscillation.  He  devised 
accordingly  an  instrument  the  oscillations  of  which  could 
be  used  while  they  lasted  as  a  measure  of  time,  and  which 
was  in  practice  found  very  useful  by  doctors  for  measuring 
the  rate  of  a  patient's  pulse. 

115.  Before  very  long  it  became  evident  that  Galilei  had 
no  special   taste  for  medicine,   a   study  selected   for   him 
chiefly  as   leading  to   a   reasonably  lucrative   professional 
career,  and  that  his  real  bent  was  for  mathematics  and  its 
applications    to   experimental   science.      He   had  received 
little  or  no  formal  teaching  in  mathematics  before  his  second 
year  at  the  University,  in  the  course  of  which  he  happened 
to  overhear  a  lesson  on  Euclid's  geometry,  given  at  the 
Grand  Duke's  court,  and  was  so  fascinated  that   he  con- 
tinued to  attend  the  course,  at  first  surreptitiously,  afterwards 
openly ;  his  interest  in  the  subject  was  thereby  so  much 
stimulated,  and  his  aptitude  for  it  was  so  marked,  that  he 
obtained  his  father's  consent  to  abandon  medicine  in  favour 
of  mathematics. 

In  1585,  however,  poverty  compelled  him  to  quit  the 
University  without  completing  the  regular  course  and 
obtaining  a  degree,  and  the  next  four  years  were  spent 


§$  ii4—ii6]          The  Pendulum :    Falling  Bodies  147 

chiefly  at  home,  where  he  continued  to  read  and  to  think 
on  scientific  subjects.      In  the  year  1586  he  wrote' his  first 
known  scientific  essay,*  which  was  circulated  in  manuscript,  i 
and  only  printed  during  the  present  century. 

1 1 6.  In  1589  he  was  appointed  for  three  years  to  a 
professorship  of  mathematics  (including  astronomy)  at  Pisa. 
A  miserable  stipend,  equivalent  to  about  five  shillings  a 
week,  was  attached  to  the  post,  but  this  he  was  to  some 
extent  able  to  supplement  by  taking  private  pupils. 

In  his  new  position  Galilei  had  scope  for  his  remarkable 
power  of  exposition,  but  far  from  being  content  with  giving 
lectures  on  traditional  lines  he  also  carried  out  a  series  of 
scientific  investigations,  important  both  in  themselves  and 
on  account  of  the  novelty  in  the  method  of  investigation 
employed. 

It  will  be  convenient  to  discuss  more  fully  at  the  end 
of  this  chapter  Galilei's  contributions  to  mechanics  and  to 
scientific  method,  and  merely  to  refer  here  briefly  to  his 
first  experiments  on  falling  bodies,  which  were  made  at  this 
time.  Some  were  performed  by  dropping  various  bodies 
from  the  top  of  the  leaning  tower  of  Pisa,  and  others  by 
rolling  balls  down  grooves  arranged  at  different  inclinations. 
It  is  difficult  to  us  nowadays,  when  scientific  experiments 
are  so  common,  to  realise  the  novelty  and  importance  at 
the  end  of  the  i6th  century  of  such  simple  experiments. 
The  mediaeval  tradition  of  carrying  out  scientific  investiga- 
tion largely  by  the  interpretation  of  texts  in  Aristotle,  Galen, 
or  other  great  writers  of  the  past,  and  by  the  deduction 
of  results  from  general  principles  which  were  to  be  found 
in  these  writers  without  any  fresh  appeal  to  observation, 
still  prevailed  almost  undisturbed  at  Pisa,  as  elsewhere. 
It  was  in  particular  commonly  asserted,  on  the  authority 
of  Aristotle,  that,  the  cause  of  the  fall  of  a  heavy  body 
being  its  weight,  a  heavier  body  must  fall  faster  than  a 
lighter  one  and  in  proportion  to  its  greater  weight.  It  may 
perhaps  be  doubted  whether  any  one  before  Galilei's  time 
had  clear  enough  ideas  on  the  subject  to  be  able  to  gi\e 
a  definite  answer  to  such  a  question  as  how  much  farther 
a  ten-pound  weight  would  fall  in  a  second  than  a  one-pound 

*  On  an  instrument  which  he  had  invented,  called  the  hydrostatic  \ 
balance. 


148  A  Short  History  of  Astronomy  [CH.  vi. 

weight ;  but  if  so  he  would  probably  have  said  that  it  would 
fall  ten  times  as  far,  or  else  that  it  would  require  ten  times 
as  long  to  fall  the  same  distance.  To  actually  try  the 
experiment,  to  vary  its  conditions,  so  as  to  remove  as  many 
accidental  causes  of  error  as  possible,  tojncrease  in  some 
way  the  time  of  the  fall  so  as  to  enable  it  to  be  measured 
with  more  accuracy,  these  ideas,  put  into  practice  by  Galilei, 
were  entirely  foreign  to  the  prevailing  habits  of  scientific 
thought,  and  were  indeed  regarded  by  most  of  his  col- 
leagues as  undesirable  if  not  dangerous  innovations.  A 
few  simple  experiments  were  enough  to  prove  the  complete 
falsity  of  the  current  beliefs  in.this  matter,  and  to  establish 
that  in  general  bodies  of  different  weights  fell  nearly  the 
same  distance  in  the  same  time,  the  difference  being  not 
more  than  co  Id  reasonably  be  ascribed  to  the  resistance 
offered  by  the  air. 

These  and  other  results  were  embodied  in  a  tract,  which, 
like  most  of  Galilei's  earlier  writings,  was  only  circulated 
in  manuscript,  the  substance  of  it  being  first  printed  in  the 
great  treatise  on  mechanics  which  he  published  towards 
the  end  of  his  life  (§  133). 

These  innovations,  coupled  with  the  slight  respect  that 
he  was  in  the  habit  of  paying  to  those  who  differed  from 
him,  evidently  made  Galilei  far  from  popular  with  his 
colleagues  at  Pisa,  and  either  on  this  account,  or  on  account 
of  domestic  troubles  consequent  on  the  death  of  his  father 
(1591),  he  resigned  his  professorship  shortly  before  the 
expiration  of  his  term  of  office,  and  returned  to  his  mother's 
home  at  Florence. 

117.  After  a  few  months  spent  at  Florence  he  was 
appointed,  by  the  influence  of  a  Venetian  friend,  to  a 
professorship  of  mathematics  at  Padua,  which  was  then  in 
the  territory  of  the  Venetian  republic  (1592).  The  ap- 
pointment was  in  the  first  instance  for  a  period  of  six  years, 
and  the  salary  much  larger  than  at  Pisa.  During  the  first 
few  years  of  Galilei's  career  at  Padua  his  activity  seems 
o  have  been  very  great  and  very  varied  ;  in  addition  to 
jiving  his  regular  lectures,  to  audiences  which  rapidly  in- 
creased, he  wrote  tracts,  for  the  most  part  not  printed  at 
the  time,  on  astronomy,  on  mechanics,  and  on  fortification, 
and  invented  a  variety  of  scientific  instruments. 


$§  H7,  "8]  First  Astronomical  Discoveries  149 

No  record  exists  of  the  exact  time  at  which  he  first 
adopted  the  astronomical  views  of  Coppernicus,  but  he 
himself  stated  that  in  1597  he  had  adopted  them  some 
years  before,  and  had  collected  arguments  in  their  support. 

In  the  following  year  his  professorship  was  renewed  for 
six  years  with  an  increased  stipend,  a  renewal  which  was 
subsequently  made  for  six  years  more,  and  finally  for  life, 
the  stipend  being  increased  on  each  occasion. 

Galilei's  first  contribution  to  astronomical  discovery  w,as 
made  in  1604,  when  a  star  appeared  suddenly  in  the  con- 
stellation Serpentarius,  and  was  shewn  by  him   to   be   at 
any  rate  more  distant  than  the  planets,  a  result  confirming 
Tycho's  conclusions  (chapter  v.,  §  100)  that  changes  take   ' 
place  in  the  celestial  regions  even  beyond  the  planets,  and   , 
are  by  no  means  confined — as  was  commonly  believed^  1 
to  the  earth  and  its  immediate  surroundings. 

1 1 8.  By  this  time  Galilei  had  become  famous  through- 
out Italy,  not  only  as  a  brilliant  lecturer,  but  also  as  a 
learned  and  original  man  of  science.  The  discoveries 
which  first  gave  him  a  European  reputation  were,  however, 
the  series  of  telescopic  observations  made  in  1609  and  the 
following  years. 

Roger  Bacon  (chapter  in.,  §  67)  had  claimed  to  have  de- 
vised a  combination  of  lenses  enabling  distant  objects  to  be 
seen  as  if  they  were  near ;  a  similar  invention  was  probably 
made  by  our  countryman  Leonard  Digges  (who  died  about 
1571),  and  was  described  also  by  the  Italian  Porta  in  1558. 
If  such  an  instrument  was  actually  made  by  any  one  of  the 
three,   which   is   not   certain,   the   discovery   at   any   rate 
attracted  no  attention  and.  was  again  lost.     The  effective  ^ 
discovery  .of  the  telescope  was  made  in  Holland  in  1608  I 
by  Hans  Lippersheim  (?-i6i9),  a  spectacle-maker  of  Middle- 1 
burg,  and  almost  simultaneously  by  two  other  Dutchmen, 
but  whether   independently  or  not  it  is  impossible  to  say. 
Early  in  the  following  year  the  report   of  the   invention 
reached  Galilei,  who,  though  without  any  detailed  informa- 
tion as  to  the  structure  of  the  instrument,  succeeded  after 
a  few  trials  in  arranging  two  lenses — one  convex  and  one 
concave — in   a    tube    in   such  a   way   as   to   enlarge   the 
apparent  size  of  an  object  looked  at ;    his  first  instrument  / 
made    objects    appear   three   times    nearer,   consequently! 


150  A  Short  History  of  Astronomy  [Cn.  vi. 

/three  times  greater  (in  breadth  and  height),  and  he  was 
^soon  able  to  make  telescopes  which  in  the  same  way 
/  magnified  thirty-fold. 

That  the  new  instrument  might  be  applied  to  celestial 
as  well  as  to  terrestrial  objects  was  a  fairly  obvious  idea, 
which  was  acted  on  almost  at  once  by  the  English  mathe- 
matician Thomas  Harriot  (1560-1621),  by  Simon  Marius 
(1570-1624) -in  Germany,  and  by  Galilei.  That  the  credit 
of  first  using  the  telescope  for  astronomical  purposes  is 
almost  invariably  attributed  to  Galilei,  though  his  first 
observations  were  in  all  probability  slightly  later  in  date 
than  those  of  Harriot  and  Marius,  is  to  a  great  extent 
justified  by  the  persistent  way  in  which  he  examined  object 
after  object,  whenever  there  seemed  any  reasonable  prospect 
of  results  following,  by  the  energy  and  acuteness  with  which 
he  followed  up  each  clue,  by  the  independence  of  mind 
with  which  he  interpreted  his  observations,  and  above  all 
by  the  insight  with  which  he  realised  their  astronomical 
importance. 

119.  His  first  series  of  telescopic  discoveries  were  pub- 
lished early  in  1610  in  a  little  book  called  Sidereus  Nuncius, 
or  The  Sidereal  Messenger.  His  first  observations  at 
once  threw  a  flood  of  light  on  the  nature  of  our  nearest 
celestial  neighbour,  the  moon.  It  was  commonly  believed 
that  the  moon,  like  the  other  celestial  bodies,  was  perfectly 
smooth  and  spherical,  and  the  cause  of  the  familiar  dark 
markings  on  the  surface  was  quite  unknown.* 

Galilei  discovered  at  once  a  number  of  smaller  markings, 
both  bright  and  dark  (fig.  53),  and  recognised  many  of 
the  latter  as  shadows  of  lunar  mountains  cast  by  the 
sun ;  and  further  identified  bright  spots  seen  near  the 
boundary  of  the  illuminated  and  dark  portions  of  the  moon 
as  mountain-tops  just  catching  the  light  of  the  rising  or 
.setting  sun,  while  the  surrounding  lunar  area  was  still  in 
darkness.  Moreover,  with  characteristic  ingenuity  and  love 

(of  precision,  He  calculated  from  observations  of  this  nature 
the  height  of  some  of  the  more  conspicuous  lunar  moun- 

*  A  fair  idea  of  mediaeval  views  on  the  subject  may  be  derived  from 
one  of  the  most  tedious  Cantos  in  Dante's  great  poem  (Paradiso,  II.), 
i  i  which  the  poet  and  Beatrice  expound  two  different  "  explanations  " 
cf  the  spots  on  the  moon. 


FIG.  53. — One  of  Galilei's  drawings  of  the  moon.     From  the 

Sidereus  Nuncius.  [To  face  p.  150. 


$$  up— i2i ]  Observations  of  the  Moon  151 

tains,  the  largest  being  estimated  by  him  to  be  about  four  j 
miles  high,  a  result  agreeing  closely  with  modern  estimates  j 
of  the  greatest  height  on  the  moon.     The  large  dark  spots  I 
he  explained  (erroneously)   as   possibly  caused  by  water, 
though  he  evidently  had  less  confidence  in  the  correctness 
of  the  explanation  than  some  of  his  immediate  scientific 
successors,   by   whom    the   name   of   seas    was    given    to  I 
these   spots  (chapter  vin.,  §  153).      He  noticed   also  the! 
absence  of  clouds.     Apart  however  from  details,  the  really  • 
significant  results  of  his  observations  were  that  the  moon 
was  in  many  important  respects  similar  to  the  earth,  that v 
the  traditional   belief  in  its  perfectly    spherical  form  had 
to  be  abandoned,  and  that  so  far  the  received  doctrine  of 
the  sharp  distinction  to  be  drawn  between  things  celestial 
and  things  terrestrial  was  shewn  to  be  without  justification  ; 
the  importance  of  this  in  connection  with  the  Coppernican 
view  that  the  earth,  instead  of  being  unique,  was  one  of 
six  planets  revolving  round  the  sun,  needs  no  comment. 

One  of  Galilei's  numerous  scientific  opponents  *  attempted 
to  explain  away  the  apparent  contradiction  between  the  old 
theory  and  the  new  observations  by  the  ingenious  sugges- 
tion that  the  apparent  valleys  in  the  moon  were  in  reality 
filled  with  some  invisible  crystalline  material,  so  that  the 
moon  was  in  fact  perfectly  spherical.  To  this  Galilei 
replied  that  the  idea  was  so  excellent  that  he  wished  to 
extend  its  application,  and  accordingly  maintained  that 
the  moon  had  on  it  mountains  of  this  same  invisible  sub- 
stance, at  least  ten  times  as  high  as  any  which  he  had 
observed. 

1 20.  The  telescope  revealed   also   the  existence  of  an 
immense   number   of  stars   too   faint  to   be   seen  by  the 
unaided   eye ;    Galilei   saw,  for  example,  36   stars  in  the 
Pleiades,   which   to   an  ordinary  eye  consist   of  six  only. 
Portions  of  the  Milky  Way  and  various  nebulous  patches 
of  light  were  also  discovered   to  consist  of  multitudes  of 
faint   stars  clustered  together;    in  the  cluster  Praesepe  (in 
the  Crab),  for  example,  he  counted  40  stars. 

121.  By  far  the  most  striking  discovery  announced  in  the 
Sidereal  Messenger  was  that  of  the  bodies  now  known  as 

*  Ludovico  delle  Colombe  in  a  tract  Contra  II  Moto  della  Terra, 
which  is  reprinted  in  the  national  edition  of  Galilei's  works,  Vol.  III. 


152  A  Short  History  of  Astronomy  [CH.  vi. 

the  moons  or  satellites  of  Jupiter.  On  January  7th,  1610, 
Galilei  turned  his  telescope  on  to  Jupiter,  and  noticed 
three  faint  stars  which  caught  his  attention  on  account  of 
*  their  closeness  to  the  planet  and  their  arrangement  nearly 
in  a  straight  line  with  it.  He  looked  again  next  night,  and 
noticed  that  they  had  changed  their  positions  relatively 
to  Jupiter,  but  that  the  change  did  not  seem  to  be  such 
as  could  result  from  Jupiter's  own  motion,  if  the  new  bodies 
were  fixed  stars.  Two  nights  later  he  was  able  to  confirm 
this  conclusion,  and  to  infer  that  the  new  bodies  were  not 
fixed  stars,  but  moving  bodies  which  accompanied  Jupiter 
in  his  movements.  A  fourth  body  was  noticed  on 
January  i3th,  and  the  motions  of  all  four  were  soon  recog- 
nised by  Galilei  as  being  motions  of  revolution  round 
Jupiter  as  a  centre.  With  characteristic  thoroughness  he 

Ori.  *  *     O          *  Occ 

FIG.  54. — Jupiter  and  its  satellites  as  seen  on  Jan.  7,  1610. 
From  the  Sidereus  Nuncius. 

watched  the  motions  of  the  new  bodies  night  after  night, 
and  by  the  date  of  the  publication  of  his  book  had  already 
estimated  with  very  fair  accuracy  their  periods  of  revolution 
round  Jupiter,  which  ranged  between  about  42  hours  and 
17  days;  and  he  continued  to  watch  their  motions  for 
years. 

The  new  bodies  were  at  first  called  by  their  discoverer 
Medicean   planets,   in   honour   of  his   patron    Cosmo   de 
Medici,  the  Grand  Duke  of  Tuscany;  but  it  was  evident 
that  bodies  revolving  round  a  planet,  as  the  planets  them- 
selves revolved  round  the  sun,  formed  a  new  class  of  bodies 
/  distinct  from  the  known  planets,  and  the  name  of  satellite, 
(  suggested  by  Kepler  as  applicable  to  the  new  bodies  as 
well  as  to  the  moon,  has  been  generally  accepted. 

The  discovery  of  Jupiter's  satellites  shewed  the  falsity 

I  of  the  old  doctrine  that  the  earth  was  the  only  centre  of 

!  motion ;    it  tended,  moreover,  seriously  to   discredit   the 

infallibility  of  Aristotle  and  Ptolemy,  who  had  clearly  no 

knowledge   of  the   existence  of  such  bodies ;   and   again 

those   who    had   difficulty   in    believing    that   Venus   and 


$  122]  The  Satellites  of  Jupiter  153 

Mercury  could  revolve  round  an  apparently  moving  body, 
the  sun,  could  not  but  have  their  doubts  shaken  when 
shewn  the  new  satellites  evidently  performing  a  motion 
of  just  this  character;  and — most  important  consequence 
of  all — the  very  real  mechanical  difficulty  involved  in  the 
Coppetnican  conception  of  the  moon  revolving  round  th< 
moving  earth  and  not  dropping  behind  was  at  any  rate 
shewn  not  to  be  insuperable,  as  Jupiter's  satellites  succeeded! 
in  performing  a  precisely  similar  feat. 

The  same  reasons  which  rendered  Galilei's  telescopic 
discoveries  of  scientific  importance  made  them  also  objec- 
tionable to  the  supporters  of  the  old  views,  and  they  were 
accordingly  attacked  in  a  number  of  pamphlets,  some  of 
which  are  still  extant  and  possess  a  certain  amount  of 
interest.  One  Martin  Horky,  for  example,  a  young  German 
who  had  studied  under  Kepler,  published  a  pamphlet  in 
which,  after  proving  to  his  own  satisfaction  that  the  satel- 
lites of  Jupiter  did  not  exist,  he  discussed  at  some  length 
what  they  were,  what  they  were  like,  and  why  they  existed. 
Another  writer  gravely  argued  that  because  the  human 
body  had  seven  openings  in  it— the  eyes,  ears,  nostrils,  and 
mouth — therefore  by  analogy  there  must  be  seven  planets 
(the  sun  and  moon  being  included)  and  no  more.  How- 
ever, confirmation  by  other  observers  was  soon  obtained 
and  the  pendulum  even  began  to  swing  in  the  opposite 
direction,  a  number  of  new  satellites  of  Jupiter  being 
announced  by  various  observers.  None  of  these,  however, 
turned  out  to  be  genuine,  and  Galilei's  four  remained  the 
only  known  satellites  of  Jupiter  till  a  few  years  ago 
(chapter  xin.,  §  295). 

122.  The  reputation  acquired  oy  Galilei  by  the  publica- 
tion of  the  Messenger  enabled  him  to  bring  to  a  satisfactory 
issue  negotiations  v\hich  he  had  for  some  time  been  carrying 
on  with  the  Tuscan  court.  Though  he  had  been  well 
treated  by  the  Venetians,  he  had  begun  to  feel  the  burden 
of  regular  teaching  somewhat  irksome,  and  was  anxious  to 
devote  more  time  to  research  and  to  writing.  A  republic 
could  hardly  be  expected  to  provide  him  with  such  a 
sinecure  as  he  wanted,  and  he  accordingly  accepted  in  the  • 
summer  of  1610  an  appointment  as  professor  at  Pisa,  and 
also  as  "  First  Philosopher  and  Mathematician  "  to  the  Grand 


154  A  Short  History  of  Astronomy  [CH.  vi. 

Duke  of  Tuscany,  with  a  handsome  salary  and  no  definite 
duties  attached  to  either  office. 

123.  Shortly  before  leaving  Padua  he  turned  his  telescope 
on  to  Saturn,  and  observed  that  the  planet  appeared  to 
consist  of  three  parts,    as   shewn   in  the   first  drawing   of 
fig.  67  (chapter   vni.,  §  154).     On   subsequent   occasions, 
however,  he  failed  to  see  more  than  the  central  body,  and 
the  appearances  of  Saturn  continued  to  present  perplexing 
variations,  till  the  mystery  was  solved  by  Huygens  in  1655 
(chapter  vni.,  §154)- 

;  The  first  discovery  made  at  Florence  (October  1610)  was 
that  Venus,  which  to  the  naked  eye  appears  to  vary  very 
much  in  brilliancy  but  not  in  shape,  was  in  reality  at  times 
crescent-shaped  like  the  new  moon  and  passed  through 
phases  similar  to  some  of  those  of  the  moon.  This  shewed 
that  Venus  was,  like  the  moon,  a  dark  body  in  itself,  deriv- 
ing its  light  from  the  sun ;  so  that  its  similarity  to  the  earth 
was  thereby  made  more  evident. 

124.  The  discovery  of  dark  spots  on  the  sun  completed 
this  series  of  telescopic  discoveries.     According  to  his  own 
statement  Galilei  first  saw  them  towards  the  end  of  1610,* 
but  apparently  paid  no  particular  attention  to  them  at  the 
time ;    and,   although    he    shewed    them    as   a   matter   of 
curiosity  to  various  friends,  he  made  no  formal  announce- 
ment of  the  discovery  till  May   1612,  by  which  time  the 
same  discovery  had  been  made  independently  by  Harriot 
(§  118)    in    England,    by  John   Fabricius  (1587-?  1615)    in 
Holland,  and  by  the  Jesuit  Christopher  Scheiner  (1575-1650) 
in  Germany,  and  had  been  published  by  Fabricius  (June 
1611).     As  a  matter  of  fact  dark  spots  had  been  seen  with 
the  naked  eye  long  before,  but  had  been  generally  supposed 
to  be  caused  by  the  passage  of  Mercury  in  front  of  the  sun. 
The  presence  on  the  sun  of  such  blemishes-as  black  spots, 
the  "  mutability  "  involved  in  their   changes  in  form  and 
position,  and  their  formation  and  subsequent  disappearance, 
were  all  distasteful   to   the   supporters  of  the   old   views, 

*  In  a  letter  of  May  4th,  1612,  he  says  that  he  has  seen  them  for 
eighteen  months;  in  the  Dialogue  on  the  Two  Systems  (III.,  p.  312, 
in  Salusbury's  translation)  he  says  that  he  saw  them  while  he  still 
lectured  at  Padua,  i.e.  presumably  by  September  1610,  as  he  moved 
to  Florence  in  that  month. 


H          L 


FIG.  55. — Sun-spots.     From  Galilei's  Macchie  Soiari. 

~T)  face  >  154. 


$§123,124]  Phases  of  Venus:   Sun-spots  155 

according  to  which  celestial  bodies  were  perfect  and  un- 
changeable. The  fact,  noticed  by  all  the  early  observers, 
that  the  spots  appeared  to  move  across  the  face  of  the  sun 
from  the  eastern  to  the  western  side  (i.e.  roughly  from  left 
to  right,  as  seen  at  midday  by  an  observer  in  our  latitudes), 
gave  at  first  sight  countenance  to  the  view,  championed  by 
Scheiner  among  others,  that  the  spots  might  really  be  small 
planets  revolving  round  the  sun,  and  appearing  as  dark 
objects  whenever  they  passed  between  the  sun  and  the 
observer.  In  three  letters  to  his  friend  Welser,  a  merchant 
prince  of  Augsburg,  written  in  1612  and  published  in  the 
following  year,*  Galilei,  while  giving  a  full  account  of  his 
observations,  gave  a  crushing  refutation  of  this  view ;  proved 
that  the  spots  must  be  on  or  close  to  the  surface  of  the 
sun,  and  that  the  motions  observed  were  exactly  such  as 
would  result  if  the  spots  were  attached  to  the  sun,  and  it 
revolved  on  an  axis  in  a  period  of  about  a  month ;  and 
further,  while  disclaiming  any  wish  to  speak  confidently, 
called  attention  to  several  of  their  points  of  resemblance 
to  clouds. 

One  of  nis  arguments  against  Schemer's  views  is  so 
simple  and  at  the  same  time  so  convincing,  that  it  may 
be  worth  while  to  reproduce  it  as  an  illustration  of  Galilei's 
method,  though  the  controversy  itself  is  quite  dead. 

Galilei  noticed,  namely,  that  while  a  spot  took  about 
fourteen  days  to  cross  from  one  side  of  the  sun  to  the 
other,  and  this  time  was  the  same  whether  the  spot  passed 
through  the  centre  of  the  sun's  disc,  or  along  a  shorter 
path  at  some  distance  from  it,  its  rate  of  motion  was  by 
no  means  uniform,  but  that  the  spot's  motion  always 
appeared  much  slower  when  near  the  edge  of  the  sun 
than  when  near  the  centre.  This  he  recognised  as  an 
effect  of  foreshortening,  which  would  result  if,  and  only  if, 
the  spot  were  near  the  sun. 

If,  for  example,  in  the  figure,  the  circle  represen^  a 
section  of  the  sun  by  a  plane  through  the  observer  at  o, 
and  A,  B,  c,  D,  E  be  points  taken  at  equal  distances  along 
the  surface  of  the  sun,  so  as  to  represent  the  positions 
of  an  object  on  the  sun  at  equal  intervals  of  time,  on 
the  assumption  that  the  sun  revolves  uniformly,  then  the 

*  Historia  e  Dimostrazioni  intorno  alle  Macchie  So/an. 


156  A  Short  History  of  Astronomy  \Cu.  vi 

apparent  motion  from  A  to  B,  as  seen  by  the  observer 
at  o,  is  measured  by  the  angle  A  o  B,  and  is  obviously 
much  less  than  that  from  D  to  E,  measured  by  the  angle 
DOE,  and  consequently  an  object  attached  to  the  sun 
must  appear  to  move  more  slowly  from  A  to  B,  i.e.  near 
the  sun's  edge,  than  from  D  to  E,  near  the  centre.  On  the 
other  hand,  if  the  spot  be  a  body  revolving  round  the  sun 
at  some  distance  from  it,  e.g.  along  the  do'.ted  circle  c  d  e> 
then  if  c,  d,  e  be  taken  at  equal  distances  from  one  another, 
the  apparent  motion  from  c  to  d,  measured  again  by  the 
angle  c  o  d,  is  only  very  slightly  less  than  that  from  d  to  e, 
measured  by  the  angle  d  o  e.  Moreover,  it  required  only 
a  simple  calculation,  performed  by  Galilei  in  several  cases, 


FIG.  56. — Galilei's  proof  that  sun-spots  are  not  planets. 

to  express  these  results  in  a  numerical  shape,  and  so  to 
infer  from  the  actual  observations  that  the  spots  could  not 
be  more  than  a  very  moderate  distance  from  the  sun.  The 
only  escape  from  this  conclusion  was  by  the  assumption 
that  the  spots,  if  they  were  bodies  revolving  round  the  sun, 
moved  irregularly,  in  such  a  way  as  always  to  be  moving 
fastest  when  they  happened  to  be  between  the  centre  of 
the  sun  and  the  earth,  whatever  the  earth's  position  might 
be  at  the  time,  a  procedure  for  which,  on  the  one  hand, 
no  sort  of  reason  could  be  given,  and  which,  on  the  other, 
was  entirely  out  of  harmony  with  the  uniformity  to  which 
mediaeval  astronomy  clung  so  firmly. 

The  rotation  of  the  sun  about  an  axis,  thus  established, 
might  evidently  have  been  used  as  an  argument  in  support 
of  the  view  that  the  earth  also  had  such  a  motion,  but, 
as  far  as  I  am  aware,  neither  Galilei  nor  any  contemporary 
noticed  the  analogy.  Among  other  facts  relating  to  the 


$  i2s]  Sun-spots  157 

spots  observed  by  Galilei  were  the  greater  darkness  of  the 
central  parts,  some  of  his  drawings  (see  fig.  55)  shewing, 
like  most  modem  drawings,  a  fairly  well-marked  line  of 
division  between  the  central  part  (or  umbra)  and  the  less 
dark  fringe  (or  penumbra)  surrounding  it ;  he  noticed  also 
that  spots  frequently  appeared  in  groups,  that  the  members 
of  a  group  changed  their  positions  relatively  to  one  another, 
that  individual  spots  changed  their  size  and  shape  con- 
siderably during  their  lifetime,  and  that  spots  were  usually 
most  plentiful  in  two  regions  on  each  side  of  the  sun's 
equator,  corresponding  roughly  to  the  tropics  on  our  own 
globe,  and  were  never  seen  far  beyond  these  limits. 

Similar  observations  were  made  by  other  telescopists, 
and  to  Scheiner  belongs  the  credit  of  fixing,  with  consider- 
ably more  accuracy  than  Galilei,  the  position  of  the  sun's 
axis  and  equator  and  the  time  of  its  rotation. 

125.  The  controversy  with  Scheiner  as  to  the  nature 
of  spots  unfortunately  developed  into  a  personal  quarrel 
as  to  their  respective  claims  to  the  discovery  of  spots, 
a  controversy  which  made  Scheiner  his  bitter  enemy,  and 
probably  contributed  not  a  little  to  the  hostility  with  which 
Galilei  was  henceforward  regarded  by  the  Jesuits.  Galilei's 
uncompromising  championship  of  the  new  scientific  ideas, 
the  slight  respect  which  he  shewed  for  established  and 
traditional  authority,  and  the  biting  sarcasms  with  which 
he  was  in  the  habit  of  greeting  his  opponents,  had  won 
for  him  a  large  number  of  enemies  in  scientific  and 
philosophic  circles,  particularly  among  the  large  party 
\\ho  spoke  in  the  name  of  Aristotle,  although,  as  Galilei 
was  never  tired  of  reminding  them,  their  methods  of 
thought  and  their  conclusions  would  in  all  probability 
have  been  rejected  by  the  great  Greek  philosopher  if  he 
had  been  alive. 

It  was  probably  in  part  owing  to  his  consciousness  of  a 
growing  hostility  to  his  views,  both  in  scientific  and  in 
ecclesiastical  circles,  that  Galilei  paid  a  short  visit  to  Rome 
in  1611,  when  he  met  with  a  most  honourable  reception 
and  was  treated  with  great  friendliness  by  several  cardinals 
and  other  persons  in  high  places. 

Unfortunately  he  soon  began  to  be  drawn  into  a  contro- 
versy as  to  the  relative  validity  in  scientific  matters  of 


158  A  Short  History  of  Astronomy  [CH.  vi. 

observation  and  reasoning  on  the  one  hand,  and  of  the 
authority  of  the  Church  and  the  Bible  on  the  other,  a 
controversy  which  began  to  take  shape  about  this  time  and 
which,  though  its  battle-field  has  shifted  from  science  to 
science,  has  lasted  almost  without  interruption  till  modern 
times. 

In  1611  was  published  a  tract  maintaining  Jupiter's 
satellites  to  be  unscriptural.  In  1612  Galilei  consulted 
Cardinal  Conti  as  to  the  astronomical  teaching  of  the  Bible, 
and  obtained  from  him  the  opinion  that  the  Bible  appeared 
to  discountenance  both  the  Aristotelian  doctrine  of  the 
immutability  of  the  heavens  and  the  Coppernican  doctrine 
of  the  motion  of  the  earth.  A  tract  of  Galilei's  on  floating 
bodies,  published  in  1612,  roused  fresh  opposition,  but  on 
the  other  hand  Cardinal  Barberini  (who  afterwards,  as 
Urban  VIII. ,  took  a  leading  part  in  his  persecution) 
specially  thanked  him  for  a  presentation  copy  of  the  book 
on  sun-spots,  in  which  Galilei,  for  the  first  time,  clearly 
proclaimed  in  public  his  adherence  to  the  Coppernican 
system.  In  the  same  year  (1613)  his  friend  and  follower, 
Father  Castelli,  was  appointed  professor  of  mathematics 
at  Pisa,  with  special  instructions  not  to  lecture  on  the 
motion  of  the  earth.  Within  a  few  months  Castelli  was 
drawn  into  a  discussion  on  the  relations  of  the  Bible  to 
astronomy,  at  the  house  of  the  Grand  Duchess,  and  quoted 
Galilei  in  support  of  his  views ;  this  caused  Galilei  to 
express  his  opinions  at  some  length  in  a  letter  to  Castelli, 
which  was  circulated  in  manuscript  at  the  court.  To  this 
a  Dominican  preacher,  Caccini,  replied  a  few  months 
afterwards  by  a  violent  sermon  on  the  text,  "  Ye  Galileans, 
why  stand  ye  gazing  up  into  heaven?"*  and  in  1615 
Galilei  was  secretly  denounced  to  the  Inquisition  on  the 
strength  of  the  letter  to  C  istelli  and  other  evidence.  In 
the  same  year  he  expanded  the  letter  to  Castelli  into  a 
more  elaborate  treatise,  in  the  form  of  a  Letter  to  the  Grand 
Duchess  Christine^  which  was  circulated  in  manuscript,  but 
not  printed  till  1636.  The  discussion  of  the  bearing  of 
particular  passages  of  the  Bible  (e.g.  the  account  of  the 
miracle  of  Joshua)  on  the  Ptolemaic  and  Coppernican 

*  Acts  i.  ii.  The  pun  is  not  quite  so  bad  in  its  Latin  form  :  Viri 
Gali!ctcil  etc. 


§  126]  The  First  Condemnation  of  Galilei  159 

systems  has  now  lost  most  of  its  interest ;  it  may,  however, 
be  worth  noticing  that  on  the  more  general  question  Galilei 
quotes  with  approval  the  saying  of  Cardinal  Baronius, 
"  That  the  intention  of  the  Holy  Ghost  is  to  teach  us  not 
how  the  heavens  go,  but  how  to  go  to  heaven,"  *  and  the 
following  passage  gives  a  good  idea  of  the  general  tenor 
of  his  argument : — 

"Methinks,  that  in  the  Discussion  of  Natural  Problemes  we 
ought  not  to  begin  at  the  authority  of  places  of  Scripture  ;  but 
at  Sensible  Experiments  and  Necessary  Demonstrations.  For 
.  .  .  Nature  being  inexorable  and  immutable,  and  never  passing 
the  bounds  of  the  Laws  assigned  her,  as  one  that  nothing  careth, 
whether  her  abstruse  reasons  and  methods  of  operating  be  or 
be  not  exposed  to  the  capacity  of  men;  I  conceive  that  that 
concerning  Natural  Effects,  which  either  sensible  experience 
sets  before  our  eyes,  or  Necessary  Demonstrations  do  prove  unto 
us,  ought  not,  upon  any  account,  to  be  called  into  question, 
much  less  condemned  upon  the  testimony  of  Texts  of  Scripture, 
which  may  under  their  words,  couch  senses  seemingly  contrary 
thereto."  t 

126.  Meanwhile  his  enemies  had  become  so  active  that 
Galilei  thought  it  well  to  go  to  Rome  at  the  end  of  1615 
to  defend  his  cause.  Early  in  the  next  year  a  body  of 
theologians  known  as  the  Qualifiers  of  the  Holy  Office 
(Inquisition),  who  had  been  instructed  to  examine  certain 
Coppernican  doctrines,  reported  : — 

"That  the  doctrine  that  the  sun  was  the  centre  of  the  world 
and  immoveable  was  false  and  absurd,  formally  heretical  and 
contrary  to  Scripture,  whereas  the  doctrine  that  the  earth  was 
not  the  centre  of  the  world  but  moved,  and  has  further  a  daily 
motion,  was  philosophically  false  and  absurd  and  theologically 
at  least  erroneous." 

In  consequence  of  this  report  it  was  decided  to  censure 
Galilei,  and  the  Pope  accordingly  instructed  Cardinal 
Bellarmine  "  to  summon  Galilei  and  admonish  him  to 

*  Sftiritui  sancto  mentem  Juisse  nos  doccrc,  quo  modo  ad  Coehitn 
calitr,  non  nil/cm,  qnomodo  Coclnrn  gradiatur. 

f  From  the  translation  by  Salisbury,  in  Vol.  I.  of  his  Mathematical 
Collections. 


160  A  Short  History  of  Astronomy  [CH.  VI. 

abandon  the  said  opinion,"  which  the  Cardinal  did.* 
Immediately  afterwards  a  decree  was  issued  condemning 
the  opinions  in  question  and  placing  on  the  well-known 
Index  of  Prohibited  Books  three  books  containing  Copper- 
nican  views,  of  which  the  De  Revolutionibus  of  Coppernicus 
and  another  were  only  suspended  "  until  they  should 
be  corrected,"  while  the  third  was  altogether  prohibited. 
The  necessary  corrections  to  the  De  Revolutionibus  were 
officially  published  in  1620,  and  consisted  only  of  a  few 
alterations  which  tended  to  make  the  essential  principles 
of  the  book  appear  as  mere  mathematical  hypotheses, 
convenient  for  calculation.  Galilei  seems  to  have  been 
on  the  whole  well  satisfied  with  the  issue  of  the  inquiry, 
as  far  as  he  was  personally  concerned,  and  after  obtaining 
from  Cardinal  Bellarmine  a  certificate  that  he  had  neither 
abjured  his  opinions  nor  done  penance  for  them,  stayed 
on  in  Rome  for  some  months  to  shew  that  he  was  in 
good  repute  there. 

127.  During  the  next  few  years  Galilei,  who  was  now 
more  than  fifty,  suffered  a  good  deal  from  ill-health  and 
was  comparatively  inactive.  He  carried  on,  however,  a 
correspondence  with  the  Spanish  court  on  a  method  of 
ascertaining  the  longitude  at  sea  by  means  of  Jupiter's 
satellites.  The  essential  problem  in  finding  the  longitude 
is  to  obtain  the  time  as  given  by  the  sun  at  the  required 
place  and  also  that  at  some  place  the  longitude  of  which 
is  known.  If,  for  example,  midday  at  Rome  occurs  an 
hour  earlier  than  in  London,  the  sun  takes  an  hour  to 
travel  from  the  meridian  of  Rome  to  that  of  London,  and 
the  longitude  of  Rome  is  15°  east  of  that  of  London. 
At  sea  it  is  easy  to  ascertain  the  local  time,  e.g.  by 
observing  when  the  sun  is  highest  in  the  sky,  but  the 
great  difficulty,  felt  in  Galilei's  time  and  long  afterwards 
(chapter  x.,  §§  197,  226),  was  that  of  ascertaining  the  time  at 
some  standard  place.  Clocks  were  then,  and  long  after- 
wards, not  to  be  relied  upon  to  keep  time  accurately  during 

*  The  only  point  of  any  importance  in  connection  with  Galilei's 
relations  with  the  Inquisition  on  which  there  seems  to  be  room  for 
any  serious  doubt  is  as  to  the  stringency  of  this  warning.  It  is 
probable  that  Galilei  was  at  the  same  time  specifically  forbidden  to 
"  hold,  teach,  or  defend  in  any  way,  whether  verbally  or  in  writing," 
the  obnoxious  doctrine. 


$12?]  The  Problem  of  Longitude  :  Comets  161 

a  long  ocean  voyage,  and  some  astronomical  means  of 
determining  the  time  was  accordingly  wanted.  Galilei's 
idea  was  that  if  the  movements  of  Jupiter's  satellites,  and 
in  particular  the  eclipses  which  constantly  occurred  when 
a  satellite  passed  into  Jupiter's  shadow,  could  be  predicted, 
then  a  table  could  be  prepared  giving  the  times,  according 
to  some  standard  place,  say  Rome,  at  which  the  eclipses 
would  occur,  and  a  sailor  by  observing  the  local  time 
of  an  eclipse  and  comparing  it  with  the  time  given  in 
the  table  could  ascertain  by  how  much  his  longitude 
differed  from  that  of  Rome.  It  is,  however,  doubtful 
whether  the  movements  of  Jupiter's  satellites  could  at  that 
time  be  predicted  accurately  enough  to  make  the  method 
practically  useful,  and  in  any  case  the  negotiations  came 
to  nothing. 

In  1618  three  comets  appeared,  and  Galilei  was  soon 
drawn  into  a  controversy  on  the  subject  with  a  Jesuit 
of  the  name  of  Grassi.  The  controversy  was  marked  by 
the  personal  bitterness  which  was  customary,  and  soon 
developed  so  as  to  include  larger  questions  of  philosophy 
and  astronomy.  Galilei's  final  contribution  to  it  was 
published  in  ^623  under  the  title  //  Saggiatore  (The 
Assayer),  which  dealt  incidentally  with  the  Coppernican 
theory,  though  only  in  the  indirect  way  which  the  edict 
of  1616  rendered  necessary.  In  a  characteristic  passage, 
for  example,  Galilei  'says  : — 

"  Since  the  motion  attributed  to  the  earth,  which  I,  as  a  pious 
and  Catholic  person,  consider  most  false,  and  not  to  exist, 
accommodates  itself  so  well  to  explain  so  many  and  such 
different  phenomena,  I  shall  not  feel  sure  .  .  .  that,  false  as  it 
is,  it  may  not  just  as  deludingly  correspond  with  the  phenomena 
of  comets  " ; 

and  again,  in  speaking  of  the  rival  systems  of  Coppernicus 
and  Tycho,  he  says  :— 

"  Then  as  to  the  Copernican  hypothesis,  if  by  the  good 
fortune  of  us  Catholics  we  had  not  been  freed  from  error 
and  our  blindness  illuminated  by  the  Highest  Wisdom,  I  do 
not  believe  that  such  grace  and  good  fortune  could  have 
been  obtained  by  means  of  the  reasons  and  observations  given 
by  Tycho." 

II 


1 62  A  Short  History  of  Astronomy  [Cn.  vi 

Although  in  scientific  importance  the  Saggiatore  ranks 
far  below  many  others  of  Galilei's  writings,  it  had  a  great 
reputation  as  a  piece  of  brilliant  controversial  writing,  and 
notwithstanding  its  thinly  veiled  Coppernicanism,  the  new 
Pope,  Urban  VIII.,  to  whom  it  was  dedicated,  was  so  much 
pleased  with  it  that  he  had  it  read  aloud  to  him  at  meals. 
The  book  must,  however,  have  strengthened  the  hands 
of  Galilei's  enemies,  and  it  was  probably  with  a  view  to 
counteracting  their  influence  that  he  went  to  Rome  next 
year,  to  pay  his  respects  to  Urban  and  congratulate  him 
on  his  recent  elevation.  The  visit  was  in  almost  every 
way  a  success ;  Urban  granted  to  him  several  friendly 
interviews,  promised  a  pension  for  his  son,  gave  him  several 
presents,  and  finally  dismissed  him  with  a  letter  of  special 
recommendation  to  the  new  Grand  Duke  of  Tuscany,  who 
had  shewn  some  signs  of  being  less  friendly  to  Galilei 
than  his  father.  On  the  other  hand,  however,  the  Pope 
refused  to  listen  to  Galilei's  request  that  the  decree  of  1616 
should  be  withdrawn. 

128.  Galilei  now  set  seriously  to  work  on  the  great 
astronomical  treatise,  the  Dialogue  on  the  Two  Chief 
Systems  of  the  World,  the  Ptolemaic  ayd  Coppernican, 
which  he  had  had  in  mind  as  long  ago  as  1610,  and  in 
which  he  proposed  to  embody  most  of  his  astronomical 
work  and  to  collect  all  the  available  evidence  bearing  on 
the  Coppernican  controversy.  The  form  of  a  dialogue  was 
chosen,  partly  for  literary  reasons,  and  still  more  because 
it  enabled  him  to  present  the  Coppernican  case  as  strongly 
as  he  wished  through  the  mouths  of  some  of  the  speakers, 
without  necessarily  identifying  his  own  opinions  with  theirs. 
The  manuscript  was  almost  completed  in  1629,  and  in  the 
following  year  Galilei  went  to  Rome  to  obtain  the  necessary 
licence  for  printing  it.  The  censor  had  some  alterations 
made  and  then  gave  the  desired  permission  for  printing  at 
Rome,  on  condition  that  the  book  was  submitted  to  him 
again  before  being  finally  printed  off.  Soon  after  Galilei's 
return  to  Florence  the  plague  broke  out,  and  quarantine 
difficulties  rendered  it  almost  necessary  that  the  book 
should  be  printed  at  Florence  instead  of  at  Rome.  This 
required  a  fresh  licence,  and  the  difficulty  experienced  in 
obtaining  it  shewed  that  the  Roman  censor  was  getting 


§$  i28,  i29]    The  Dialogue  on  the  Two  Chief  Systems        163 

more  and  more  doubtful  about  the  book.  Ultimately, 
however,  the  introduction  and  conclusion  having  been  sent 
to  Rome  for  approval  and  probably  to  some  extent  re- 
written there,  and  the  whole  work  having  been  approved 
by  the  Florentine  censor,  the  book  was  printed  and  the 
first  copies  were  ready  early  in  1632,  bearing  both  the 
Roman  and  the  Florentine  imprimatur. 

129.  The  Dialogue  extends  over  four  successive  days, 
and  is  carried  on  by  three  speakers,  of  whom  Salviati  is  a 
Coppernican  and  Simplicio  an  Aristotelian  philosopher, 
while  Sagredo  is  avowedly  neutral,  but  on  almost  every 
occasion  either  agrees  with  Salviati  at  once  or  is  easily 
convinced  by  him,  and  frequently  joins  in  casting  ridicule 
upon  the  arguments  of  the  unfortunate  Simplicio.  Though 
many  of  the  arguments  have  now  lost  their  immediate 
interest,  and  the  book  is  unduly  long,  it  is  still  very  read- 
able, and  the  specimens  of  scholastic  reasoning  put  into 
the  mouth  of  Simplicio  and  the  refutation  of  them  by 
the  other  speakers  strike  the  modern  reader  as  excellent 
fooling. 

Many  of  the  arguments  used  had  been  published  by 
Galilei  in  earlier  books,  but  gain  impressiveness  and  cogency 
by  being  collected  and  systematically  arranged.  The 
Aristotelian  dogma  of  the  immutability  of  the  celestial 
bodies  is  once  more  belaboured,  and  shewn  to  be  not 
only  inconsistent  with  observations  of  the  moon,  the  sun, 
comets,  and  new  stars,  but  to  be  in  reality  incapable  of 
being  stated  in  a  form  free  from  obscurity  and  self-con- 
tradiction. The  evidence  in  favour  of  the  earth's  motion 
derived  from  the  existence  of  Jupiter's  satellites  and  from 
the  undoubted  phases  of  Venus,  from  the  suspected  phases 
of  Mercury  and  from  the  variations  in  the  apparent  size  of 
Mars,  are  once  more  insisted  on.  The  greater  simplicity 
of  the  Coppernican  explanation  of  the  daily  motion  of  the 
celestial  sphere  and  of  the  motion  of  the  planets  is  forcibly 
urged  and  illustrated  in  detail.  It  is  pointed  out  that  on 
the  Coppernican  hypothesis  all  motions  of  revolution  or 
rotation  take  place  in  the  same  direction  (from  west  to 
east),  whereas  the  Ptolemaic  hypothesis  requires  some 
to  be  in  one  direction,  some  in  another.  Moreover  the 
apparent  daily  motion  of  the  stars,  which  appears  simple 


1 64  A  Short  History  of  Astronomy  [CH.  VI. 

enough  if  the  stars  are  regarded  as  rigidly  attached  to  a 
material  sphere,  is  shewn  in  a  quite  different  aspect  if, 
as  even  Simplicio  admits,  no  such  sphere  exists,  and  each 
star  moves  in  some  sense  independently.  A  star  near  the 
pole  must  then  be  supposed  to  move  far  more  slowly  than 
one  near  the  equator,  since  it  describes  a  much  smaller 
circle  in  the  same  time  ;  and  further — an  argument  very 
characteristic  of  Galilei's  ingenuity  in  drawing  conclusions 
from  known  facts — owing  to  the  precession  of  the  equinoxes 
(chapter  n.,  §  42,  and  iv.,  §  84)  and  the  consequent  change 
of  the  position  of  the  pole  among  the  stars,  some  of  those 
stars  which  in  Ptolemy's  time  were  describing  very  small 
circles,  and  therefore  moving  slowly,  must  now  be  describing 
large  ones  at  a  greater  speed,  and  vice  versa.  An  extremely 
complicated  adjustment  of  motions  becomes  therefore 
necessary  to  account  for  observations  which  Coppernicus 
explained  adequately  by  the  rotation  of  the  earth  and  a 
simple  displacement  of  its  axis  of  rotation. 

Salviati  deals  also  with  the  standing  difficulty  that  the 
annual  motion  of  the  earth  ought  to  cause  a  corresponding 
apparent  motion  of  the  stars,  and  that  if  the  stars  be 
assumed  so  far  off  that  this  motion  is  imperceptible,  then 
some  of  the  stars  themselves  must  be  at  least  as  large  as 
the  earth's  orbit  round  the  sun.  Salviati  points  out  that 
the  apparent  or  angular  magnitudes  of  the  fixed  stars, 
avowedly  difficult  to  determine,  are  in  reality  almost  entirely 
illusory,  being  due  in  great  part  to  an  optical  effect  known 
/as  irradiation,  in  virtue  of  which  a  bright  object  always 
1  tends  to  appear  enlarged ;  *  and  that  there  is  in  consequence 
no  reason  to  suppose  the  stars  nearly  as  large  as  they  might 
otherwise  be  thought  to  be.  It  is  suggested  also  that  the 
most  promising  way  of  detecting  the  annual  motion  of  stars 
resulting  from  the  motion  of  the  earth  would  be  by 
observing  the  relative  displacement  of  two  stars  close 
together  in  the  sky  (and  therefore  nearly  in  the  same  direc- 
tion), of  which  one  might  be  presumed  from  its  greater 

*  This  is  illustrated  by  the  well-known  optical  illusion  whereby  a 
white  circle  on  a  black  background  appears  larger  than  an  equal 
black  one  on  a  white  background.  The  apparent  size  of  the  hot 
filament  in  a  modern  incandescent  electric  lamp  is  another  good 
illustration. 


$  iso]         The  Dialogue  on  the  Two  Chief  Systems          165. 

brightness  to  be  nearer  than  the  other.  It  is,  for  example, 
evident  that  if,  in  the  figure,  E,  E'  represent  two  positions  of 
the  earth  in  its  path  round  the  sun,  and  A,  B  two  stars  at 
different  distances,  but  nearly  in  the  same  direction,  then 
to  the  observer  at  E  the  star  A  appears  to  the  left  of  B, 
whereas  six  months  afterwards,  when  the  observer  is  at  E', 
A  appears  to  the  right  of  B.  Such  a  motion  of  one  star  with 
respect  to  another  close  to  it  would  be  much  more  easily 
observed  than  an  alteration  of  the  same  amount  in  the 
distance  of  the  star  from  some  standard  point  such  as  the 
pole.  Salviati  points  out  that  accurate  observations  of 


E 

FIG.  57.— The  differential  method  of  parallax. 

this  kind  had  not  been  made,  and  that  the  telescope  might 
be  of  assistance  for  the  purpose.  This  method,  known  as 
the  double-star  or  differential  method  of  parallax,  was  in 
fact  the  first  to  lead — two  centuries  later— to  a  successful 
detection  of  the  motion  in  question  (chapter  xin.,  §  278). 

130.  Entirely  new  ground  is  broken  in  the  Dialogue 
when  Galilei's  discoveries  of  the  laws  of  motion  of  bodies 
are  applied  to  the  problem  of  the  earth's  motion.  His 
great  discovery,  which  threw  an  entirely  new  light  on  the 
mechanics  of  the  solar  system,  was  substantially  the  law 
afterwards  given  by  Newton  as  the  first  of  his  three  laws 
of  motion,  in  the  form  :  Every  body  continues  in  its  state  of 
rest  or  of  uniform  motion  in  a  straight  line,  except  in  so  far 
as  it  is  compelled  by  force  appl'ed  to  it  to  change  that  state. 
Putting  aside  for  the  present  any  discussion  of  force^  a 
conception  first  made  really  definite  by  Newton,  and  only 
imperfectly  grasped  by  Galilei,  we  may  interpret  this  law 
as  meaning  that  a  body  has  no  more  inherent  tendency  to 
diminish  its  motion  or  to  stop  than  it  has  to  increase  its 
motion  or  to  start,  and  that  any  alteration  in  either  the 
speed  or  the  direction  of  a  body's  motion  is  to  be  explained 
by  the  action  on  it  of  some  other  body,  or  at  any  rate  by 


1 66  A  Short  History  of  Astronomy  [CH.  VI. 

some  other  assignable  cause.  Thus  a  stone  thrown  along 
a  road  comes  to  rest  on  account  of  the  friction  between 
it  and  the  ground,  a  ball  thrown  up  into  the  air  ascends 
more  and  more  slowly  and  then  falls  to  the  ground  on  account 
of  that  attraction  of  the  earth  on  it  which  we  call  its 
weight.  As  it  is  impossible  to  entirely  isolate  a  body  from 
all  others,  we  cannot  experimentally  realise  the  state  of 
things  in  which  a  body  goes  on  moving  indefinitely  in  the 
same  direction  and  at  the  same  rate ;  it  may,  however, 
be  shewn  that  the  more  we  remove  a  body  from  the 
influence  of  others,  the  less  alteration  is  there  in  its  motion. 
The  law  is  therefore,  like  most  scientific  laws,  an  abstrac- 
tion referring  to  a  state  of  things  to  which  we  may 
approximate  in  nature.  Galilei  introduces  the  idea  in  the 
Dialogue  by  means  of  a  ball  on  a  smooth  inclined  plane. 
If  the  ball  is  projected  upwards,  its  motion  is  gradually 
retarded ;  if  downwards,  it  is  continually  accelerated.  This 
is  true  if  the  plane  is  fairly  smooth — like  a  well-planed 
plank — and  the  inclination  of  the  plane  not  very  small. 
If  we  imagine  the  experiment  performed  on  an  ideal  plane, 
which  is  supposed  perfectly  smooth,  we  should  expect  the 
same  results  to  follow,  however  small  the  inclination  of 
the  plane.  Consequently,  if  the  plane  were  quite  level, 
so  that  there  is  no  distinction  between  up  and  down,  we 
should  expect  the  motion  to  be  neither  retarded  nor 
accelerated,  but  to  continue  without  alteration.  Other 
more  familiar  examples  are  also  given  of  the  tendency 
of  a  body,  when  once  in  motion,  to  continue  in  motion, 
as  in  the  case  of  a  rider  whose  horse  suddenly  stops,  or  of 
bodies  in  the  cabin  of  a  moving  ship  which  have  no  tendency 
to  lose  the  motion  imparted  to  them  by  the  ship,  so  that, 
e.g.,  a  body  falls  down  to  all  appearances  exactly  as  if  the 
rest  of  the  cabin  were  at  rest,  and  therefore,  in  reality, 
while  falling  retains  the  forward  motion  which  it  shares 
with  the  ship  and  its  contents.  Salviati  states  also  that — 
contrary  to  general  belief — a  stone  dropped  from  the  mast- 
head of  a  ship  in  motion  falls  at  the  foot  of  the  mast,  not 
behind  it,  but  there  is  no  reference  to  the  experiment 
having  been  actually  performed. 

This   mechanical    principle    being   once    established,    it 
becomes  easy  to  deal  with  several  common  objections  to 


i3o]          The  Dialogue  on  the  Two  Chief  Systems         167 

the  supposed  motion  of  the  earth.  The  case  of  a  stone 
dropped  from  the  top  of  a  tower,  which  if  the  earth  be 
in  reality  moving  rapidly  from  west  to  east  might  be 
expected  to  fall  to  the  west  in  its  descent,  is  easily  shewn 
to  be  exactly  parallel  to  the  case  of  a  stone  dropped  from 
the  mast-head  of  a  ship  in  motion.  The  motion  towards 
the  east,  which  the  stone  when  resting  on  the  tower  shares 
with  the  tower  and  the  earth,  is  not  destroyed  in  its 
descent,  and  it  is  therefore  entirely  in  accordance  with  the 
Coppernican  theory  that  the  stone  should  fall  as  it  does  at 
the  foot  of  the  tower.*  Similarly,  the  fact  that  the  clouds, 
the  atmosphere  in  general,  birds  flying  in  it,  and  loose 
objects  on  the  surface  of  the  earth,  shew  no  tendency  to 
be  left  behind  as  the  earth  moves  rapidly  eastward,  but 
are  apparently  unaffected  by  the  motion  of  the  earch,  is 
shewn  to  be  exactly  parallel  to  the  fact  that  the  flies  in 
a  ship's  cabin  and  the  loose  objects  there  are  in  no  way 
affected  by  the  uniform  onward  motion  of  the  ship  (though 
the  irregular  motions  of  pitching  and  rolling  do  affect  them). 
The  stock  objection  that  a  cannon-ball  shot  westward 
should,  on  the  Coppernican  hypothesis,  carry  farther  than 
one  shot  eastward  under  like  conditions,  is  met  in  the 
same  way ;  but  it  is  further  pointed  out  that,  owing  to 
the  imperfection  of  gunnery  practice,  the  experiment  could 
not  really  be  tried  accurately  enough  to  yield  any  decisive 
result. 

The  most  unsatisfactory  part  of  the  Dialogue  is  the 
fourth  day's  discussion,  on  the  tides,  of  which  Galilei 
suggests  with  great  confidence  an  explanation  based  merely 
on  the  motion  of  the  earth,  while  rejecting  with  scorn  the 
suggestion  of  Kepler  and  others — correct  as  far  as  it 
went — that  they  were  caused  by  some  influence  emanating 
from  the  moon.  It  is  hardly  to  be  wondered  at  that  the 
rudimentary  mechanical  and  mathematical  knowledge  at 
Galilei's  command  should  not  have  enabled  him  to  deal 

*  Actually,  since  the  top  of  the  tower  is  describing  a  slightly  larger 
circle  than  its  foot,  the  stone  is  at  first  moving  eastward  slightly 
faster  than  the  foot  of  the  tower,  and  therefore  should  reach  the 
ground  slightly  to  the  east  of  it.  This  displacement  is,  however, 
very  minute,  and  can  only  be  detected  by  more  delicate  experiments 
than  any  devised  by  Galilei. 


1 68  A  Short  History  of  Astronomy  [Cu.  vi. 

correctly  with  a  problem  of  which  the  vastly  more  powerful 
resources  of  modern  science  can  only  give  an  imperfect 
solution  (cf.  chapter  XL,  §  248,  and  chapter  XIIL,  §  292). 

131.  The  book  as  a  whole  was  in  effect,  though  not  in 
form,  a  powerful — indeed  unanswerable — plea  for  Copper- 
nicanism.  Galilei  tried  to  safeguard  his  position,  partly 
by  the  use  of  dialogue,  and  partly  by  the  very  remarkable 
introduction,  which  was  not  only  read  and  approved  by  the 
licensing  authorities,  but  was  in  all  probability  in  part 
the  composition  of  the  Roman  censor  and  of  the  Pope. 
It  reads  to  us  like  a  piece  of  elaborate  and  thinly  veiled 
irony,  and  it  throws  a  curious  light  on  the  intelligence 
or  on  the  seriousness  of  the  Pope  and  the  censor,  that 
they  should  have  thus  approved  it : — 

"Judicious  reader,  there  was  published  some  years  since  in 
Rome  a  salutiferous  Edict,  that,  for  the  obviating  of  the  dangerous 
Scandals  of  the  present  Age,  imposed  a  reasonable  Silence  upon 
the  Pythagorean  Opinion  of  the  Mobility  of  the  Earth.  There 
want  not  such  as  unadvisedly  affirm,  that  the  Decree  was  not 
the  production  of  a  sober  Scrutiny,  but  of  an  informed  passion  ; 
and  one  may  hear  some  mutter  that  Consultors  altogether 
ignorant  of  Astronomical  observations  ought  not  to  clipp  the 
wings  of  speculative  wits  with  rash  prohibitions.  My  zeale 
cannot  keep  silence  when  I  hear  these  inconsiderate  complaints. 
I  thought  fit,  as  being  thoroughly  acquainted  with  that  prudent 
Determination,  to  appear  openly  upon  the  Theatre  of  the  World 
as  a  Witness  of  the  naked  Truth.  I  was  at  that  time  in  Rome, 
and  had  not  only  the  audiences,  but  applauds  of  the  most 
Eminent  Prelates  of  that  Court ;  nor  was  that  Decree  published 
without  Previous  Notice  given  me  thereof.  Therefore  it  is  my 
resolution  in  the  present  case  to  give  Foreign  Nations  to  see, 
that  this  point  is  as  well  understood  in  Italy,  and  particularly 
in  Rome,  as  Transalpine  Diligence  can  imagine  it  to  be  :  and 
collecting  together  all  the  proper  speculations  that  concerne  the 
Copernican  Systeme  to  let  them  know,  that  the  notice  of  all 
preceded  the  Censure  of  the  Roman  Court  \  and  that  there 
proceed  from  this  Climate  not  only  Doctrines  for  the  health  of 
the  Soul,  but  also  ingenious  Discoveries  for  the  recreating  of 
the  Mind.  ...  I  hope  that  by  these  considerations  the  world 
will  know,  that  if  other  Nations  have  Navigated  more  than  we, 
we  have  not  studied  less  than  they  ;  and  that  our  returning  to 
assert  the  Earth's  stability,  and  to  take  the  contrary  only  for 
a  Mathematical  Capriccio,  proceeds  not  from  inadvertency  of 
what  others  have  thought  thereof,  but  (had  one  no  other 


$$  i3i,  132]  Galilei's  Trial  169 

inducements),  from  these  reasons  that  Piety,  Religion,  the 
Knowledge  of  the  Divine  Omnipotency,  and  a  consciousness 
of  the  incapacity  of  man's  understanding  dictate  unto  us."  * 

132.  Naturally  Galilei's  many  enemies  were  not  long  in 
penetrating  these  thin  disguises,  and  the  immense  success 
of  the  book  only  intensified  the  opposition  which  it  excited  ; 
the  Pope  appears  to  have  been  persuaded  that  Simplicio — 
the  butt  of  the  whole  dialogue — was  intended  for  himself, 
a  supposed  insult  which  bitterly  wounded  his  vanity ;  and 
it  was  soon  evident  that  the  publication  of  the  book  could 
not  be  allowed  to  pass  without  notice.  In  June  1632  a 
special  commission  was  appointed  to  inquire  into  the 
matter — an  unusual  procedure,  probably  meant  as  a  mark 
of  consideration  for  Galilei — and  two  months  later  the 
further  issue  of  copies  of  the  book  was  prohibited,  and  in 
September  a  papal  mandate  was  issued  requiring  Galilei 
to  appear  personally  before  the  Inquisition.  He  was  evi- 
dently frightened  by  the  summons,  and  tried  to  avoid  com- 
pliance through  the  good  offices  of  the  Tuscan  court  and 
by  pleading  his  age  and  infirmities,  but  after  considerable 
delay,  at  the  end  of  which  the  Pope  issued  instructions  to 
bring  him  if  necessary  by  force  and  in  chains,  he  had 
to  submit,  and  set  off  for  Rome  early  in  1633.  Here  he 
was  treated  with  unusual  consideration,  for  whereas  in 
general  even  the  most  eminent  offenders  under  trial  by  the 
Inquisition  were  confined  in  its  prisons,  he  was  allowed  to 
live  with  his  friend  Niccolini,  the  Tuscan  ambassador, 
throughout  the  trial,  with  the  exception  of  a  period  of 
about  three  weeks,  which  he  spent  within  the  buildings 
of  the  Inquisition,  in  comfortable  rooms  belonging  to  one  of 
the  officials,  with  permission  to  correspond  with  his  friends, 
to  take  exercise  in  the  garden,  and  other  privileges.  At 
his  first  hearing  before  the  Inquisition,  his  reply  to  the 
charge  of  having  violated  the  decree  of  1616  (§  126)  was 
that  he  had  not  understood  that  the  decree  or  the  admoni- 
tion given  to  him  forbade  the  teaching  of  the  Coppernican 
theory  as  a  mere  "  hypothesis,"  and  that  his  book  had  not 
upheld  the  doctrine  in  any  other  way.  Between  his  first 
and  second  hearing  the  Commission,  which  had  been 

*  From  the  translation  by  Salusbury,  in  Vol.  1.  of  his  Mathematical 
Collections. 


170  A  Short  History  of  Astronomy  [CH.  vi. 

examining  his  book,  reported  that  it  did  distinctly  defend 
and  maintain  the  obnoxious  doctrines,  and  Galilei,  having 
been  meanwhile  privately  advised  by  the  Commissary- 
General  of  the  Inquisition  to  adopt  a  more  submissive 
attitude,  admitted  at  the  next  hearing  that  on  reading  his 
book  again  he  recognised  that  parts  of  it  gave  the  arguments 
for  Coppernicanism  more  strongly  than  he  had  at  first 
thought.  The  pitiable  state  to  which  he  had  been  reduced 
was  shewn  by  the  offer  which  he  now  made  to  write  a 
continuation  to  the  Dialogue  which  should  as  far  as  possible 
refute  his  own  Coppernican  arguments.  At  the  final 
hearing  on  June  2ist  he  was  examined  under  threat  of 
torture,*  and  on  the  next  day  he  was  brought  up  for 
sentence.  He  was  convicted  "  of  believing  and  holding 
the  doctrines — false  and  contrary  to  the  Holy  and  Divine 
Scriptures — that  the  sun  is  the  centre  of  the  world,  and 
that  it  does  not  move  from  east  to  west,  and  that  the  earth 
does  move  and  is  not  the  centre  of  the  world ;  also  that  an 
opinion  can  be  held  and  supported  as  probable  after  it  has 
been  declared  and  decreed  contrary  to  the  Holy  Scriptures." 
In  punishment,  he  was  required  to  "abjure,  curse,  and 
detest  the  aforesaid  errors,"  the  abjuration  being  at  once 
read  by  him  on  his  knees ;  and  was  further  condemned  to 
the  "  formal  prison  of  the  Holy  Office  "  during  the  pleasure 
of  his  judges,  and  required  to  repeat  the  seven  penitential 
psalms  once  a  week  for  three  years.  On  the  following  day 
the  Pope  changed  the  sentence  of  imprisonment  into  con- 
finement at  a  country-house  near  Rome  belonging  to  the 
Grand  Duke,  and  Galilei  moved  there  on  June  24th.t  On 
petitioning  to  be  allowed  to  return  to  Florence,  he  was  at 
first  allowed  to  go  as  far  as  Siena,  and  at  the  end  of  the 
year  was  permitted  to  retire  to  his  country-house  at  Arcetri 
near  Florence,  on  condition  of  not  leaving  it  for  the  future 
without  permission,  while  his  intercourse  with  scientific  and 
other  friends  was  jealously  watched. 

*  The  official  minute  is :  Et  ei  dicto  quod  dicat  veritatem,  alias 
devenietur  ad  torturam. 

f  The  three  days  June  21-24  are  the  only  ones  which  Galilei 
could  have  spent  in  an  actual  prison,  and  there  seems  no  reason  to 
suppose  that  they  were  spent  elsewhere  than  in  the  comfortable 
rooms  in  which  it  is  known  that  he  lived  during  most  of  April. 


[To  face  p,  171. 


$  132]  The  Second  Condemnation  of  Galilei  171 

The  story  of  the  trial  reflects  little  credit  either  on 
Galilei  or  on  his  persecutors.  For  the  latter,  it  may  be 
urged  that  they  acted  with  unusual  leniency  considering 
the  customs  of  the  time ;  and  it  is  probable  that  many 
of  those  who  were  concerned  in  the  trial  were  anxious  to 
do  as  little  injury  to  Galilei  as  possible,  but  were  practically 
forced  by  the  party  personally  hostile  to  him  to  take  some 
notice  of  the  obvious  violation  of  the  decree  of  1616.  It 
is  easy  to  condemn  Galilei  for  cowardice,  but  it  must  be 
borne  in  mind,  on  the  one  hand,  that  he  was  at  the  time 
nearly  seventy,  and  much  shaken  in  health,  and,  on  the 
other,  that  the  Roman  Inquisition,  if  not  as  cruel  as  the 
Spanish,  was  a  very  real  power  in  the  early  iyth  century  ; 
during  Galilei's  life-time  (1600)  Giordano  Bruno  had  been 
burnt  alive  at  Rome  for  writings  which,  in  addition  to 
containing  religious  and  political  heresies,  supported  the 
Coppernican  astronomy  and  opposed  the  traditional 
Aristotelian  philosophy.  Moreover,  it  would  be  unfair  to 
regard  his  submission  as  due  merely  to  considerations  of 
personal  safety,  for — apart  from  the  question  whether  his 
beloved  science  would  have  gained  anything  by  his  death 
or  permanent  imprisonment — there  can  be  no  doubt  that 
Galilei  was  a  perfectly  sincere  member  of  his  Church,  and 
although  he  did  his  best  to  convince  individual  officers 
of  the  Church  of  the  correctness  of  his  views,  and  to 
minimise  the  condemnation  of  them  passed  in  1616,  yet 
he  was  probably  prepared,  when  he  found  that  the  con- 
demnation was  seriously  meant  by  the  Pope,  the  Holy 
Office,  and  others,  to  believe  that  in  some  senses  at  least 
his  views  must  be  wrong,  although,  as  a  matter  of  observa- 
tion and  pure  reason,  he  was  unable  to  see  how  or  why. 
In  fact,  like  many  other  excellent  people,  he  kept  water- 
tight compartments  in  his  mind,  respect  for  the  Church 
being  in  one  and  scientific  investigation  in  another. 

Copies  of  the  sentence  on  Galilei  and  of  his  abjuration 
were  at  once  circulated  in  Italy  and  in  Roman  Catholic 
circles  elsewhere,  and  a  decree  of  the  Congregation  of  the 
Index  was  also  issued  adding  the  Dialogue  to  the  three 
Coppernican  books  condemned  in  1616,  and  to  Kepler's 
Epitome  of  the  Coppernican  Astronomy  (chapter  VH.,  §  145), 
which  had  been  put  on  the  Index  shortly  afterwards.  It 


172  A  Short  History  of  Astrorioniy      [Cn.  VI.,  %  133 

may  be  of  interest  to  note  that  these  five  books  still  remained 
in  the  edition  of  the  Index  of  Prohibited  Books  which  was 
issued  in  1819  (with  appendices  dated  as  late  as  1821), 
but  disappeared  from  the  next  edition,  that  of  1835. 

133.  The  rest  of  Galilei's  life  may  be  described  very 
briefly.  With  the  exception  of  a  few  months,  during  which 
he  was  allowed  to  be  at  Florence  for  the  sake  of  medical 
treatment,  he  remained  continuously  at  Arcetri,  evidently 
pretty  closely  watched  by  the  agents  of  the  Holy  Office, 
much  restricted  in  his  intercourse  with  his  friends,  and 
prevented  from  carrying  on  his  studies  in  the  directions 
which  he  liked  best.  He  was  moreover  very  infirm,  and 
he  was  afflicted  by  domestic  troubles,  especially  by  the 
death  in  1634  of  his  favourite  child,  a  nun  in  a  neighbouring 
convent.  But  his  spirit  was  not  broken,  and  he  went  on 
with  several  important  pieces  of  work,  which  he  had  begun 
earlier  in  his  career.  He  carried  a  little  further  the  study 
of  his  beloved  Medicean  Planets  and  of  the  method  of  finding 
longitude  based  on  their  movements  (§127),  and  negotiated 
on  the  subject  with  the  Dutch  government.  He  made  also 
a  further  discovery  relating  to  the  moon,  of  sufficient 
importance  to  deserve  a  few  words  of  explanation. 

It  had  long  been  well  known  that  as  the  moon  describes 
her  monthly  path  round  the  earth  we  see  the  same  markings 
substantially  in  the  same  positions  on  the  disc,  so  that 
substantially  the  same  face  of  the  moon  is  turned  towards 
the  earth.  It  occurred  to  Galilei  to  inquire  whether  this 
was  accurately  the  case,  or  whether,  on  the  contrary,  some 
change  in  the  moon's  disc  could  be  observed.  He  saw 
that  if,  as  seemed  likely,  the  line  joining  the  centres  of  the 
earth  and  moon  always  passed  through  the  same  point 
on  the  moon's  surface,  nevertheless  certain  alterations  in 
an  observer's  position  on  the  earth  would  enable  him  to 
see  different  portions  of  the  moon's  surface  from  time  to 
time.  The  simplest  of  these  alterations  is  due  to  the  daily 
motion  of  the  earth.  Let  us  suppose  for  simplicity  that 
the  observer  is  on  the  earth's  equator,  and  that  the  moon  is 
at  the  time  in  the  celestial  equator.  Let  the  larger  circle 
in  fig.  58  represent  the  earth's  equator,  and  the  smaller 
circle  the  section  of  the  moon  by  the  plane  of  the  equator. 
Then  in  about  12  hours  the  earth's  rotation  carries  the 


174  A  Short  History  of  Astronomy  [CH.  vi. 

observer  from  A,  where  he  sees  the  moon  rising,  to  B,  where 
he  sees  it  setting.  When  he  is  at  c,  on  the  line  joining  the 
centres  of  the  earth  and  moon,  the  point  o  appears  to  be  in 
the  centre  of  the  moon's  disc,  and  the  portion  CQ  c'  is  visible, 
c  R  c  invisible.  But  when  the  observer  is  at  A,  the  point  P, 
on  the  right  of  o,  appears  in  the  centre,  and  the  portion 
a  P  a'  is  visible,  so  that  c'  a'  is  now  visible  and  a  c  invisible. 
In  the  same  way,  when  the  observer  is  at  B,  he  can  see  the 
portion  c  b,  while  b'  c '  is  invisible  and  Q  appears  to  be  in 
the  centre  of  the  disc.  Thus  in  the  course  of  the  day 
the  portion  a  o  b'  (dotted  in  the  figure)  is  constantly  visible 
and  b  R  a!  (also  dotted)  constantly  invisible,  while  a  c  b 
and  a'  c  b'  alternately  come  into  view  and  disappear.  In 
other  words,  when  the  moon  is  rising  we  see  a  little 
more  of  the  side  which  is  the  then  uppermost,  and  when 
she  is  setting  we  see  a  little  more  of  the  other  side  which  is 
uppermost  in  this  position.  A  similar  explanation  applies 
when  the  observer  is  not  on  the  earth's  equator,  but  the 
geometry  is  slightly  more  complicated.  In  the  same  way,  as 
the  moon  passes  from  south  to  north  of  the  equator  and  back 
as  she  revolves  round  the  earth,  we  see  alternately  more  and 
less  of  the  northern  and  southern  half  of  the  moon.  This 
set  of  changes — the  simplest  of  several  somewhat  similar 
ones  which  are  now  known  as  librations  of  the  moon — being 
thus  thought  of  as  likely  to  occur,  Galilei  set  to  work  to  test 
their  existence  by  observing  certain  markings  of  the  moon 
usually  visible  near  the  edge,  and  at  once  detected  altera- 
tions in  their  distance  from  the  edge,  which  were  in  general 
accordance  with  his  theoretical  anticipations.  A  more 
precise  inquiry  was  however  interrupted  by  failing  sight, 
culminating  (at  the  end  of  1636)  in  total  blindness. 

But  the  most  important  work  of  these  years  was  the 
completion  of  the  great  book,  in  which  he  summed  up 
and  completed  his  discoveries  in  mechanics,  Mathe- 
matical Discourses  and  Demonstrations  concerning  Two 
New  Sciences,  relating  to  Mechanics  and  to  Local  Motion. 
It  was  written  in  the  form  of  a  dialogue  between  the  same 
three  speakers  who  figured  in  the  Dialogue  on  the  Systems, 
but  is  distinctly  inferior  in  literary  merit  to  the  earlier 
work.  We  have  here  no  concern  with  a  large  part  of 
the  book,  which  deals  with  the  conditions  under  which 


$  i33]  Libration :  the  Two  New  Sciences  175 

bodies  are  kept  at  rest  by  forces  applied  to  them  (statics), 
and  certain  problems  relating  to  the  resistance  of  bodies 
to  fracture  and  to  bending,  though  in  both  of  these 
subjects  Galilei  broke  new  ground.  More  important 
astronomically — and  probably  intrinsically  also — is  what  he 
calls  the  science  of  local  motion,*  which  deals  with  the 
motion  of  bodies.  He  builds  up  on  the  basis  of  his  early 
experiments  (§  116)  a  theory  of  falling  bodies,  in  which 
occurs  for  the  first  time  the  important  idea  of  uniformly 
accelerated  motion,  or  uniform  acceleration,  i.e.  motion 
in  which  the  moving  body  receives  in  every  equal  interval 
of  time  an  equal  increase  of  velocity.  He  shews  that  the 
motion  of  a  falling  body  is — except  in  so  far  as  it  is  dis- 
turbed by  the  air — of  this  nature,  and  that,  as  already 
stated,  the  motion  is  the  same  for  all  bodies,  although 
his  numerical  estimate  is  not  at  all  accurate.t  From  this 
fundamental  law  he  works  out  a  number  of  mathematical 
deductions,  connecting  the  space  fallen  through,  the  velocity, 
and  the  time  elapsed,  both  for  the  case  of  a  body  falling 
freely  and  for  one  falling  down  an  inclined  plane.  He 
gives  also  a  correct  elementary  theory  of  projectiles,  in 
the  course  of  which  he  enunciates  more  completely  than 
before  the  law  of  inertia  already  referred  to  (§  130), 
although  Galilei's  form  is  still  much  less  general  than 
Newton's : — 

Conceive  a  body  projected  or  thrown  along  a  horizontal 
plane ,  all  impediments  being  removed.  Now  it  is  clear  by 
what  we  have  said  before  at  length  that  its  motion  will 
be  uniform  and  perpetual  along  the  said  plane^  if  the  plane 
extend  indefinitely. 

In  connection  with  projectiles,  Galilei  also  appears  to 
realise  that  a  body  may  be  conceived  as  having  motions 
in  two  different  directions  simultaneously,  and  that  each 
may  be  treated  as  independent  of  the  other,  so  that, 
for  example,  if  a  bullet  is  shot  horizontally  out  of  a 
gun,  its  downward  motion,  due  to  its  weight,  is  unaffected 

*  Equivalent  to  portions  of  the  subject  now  called  dynamics  or 
(more  correctly)  kinematics  and  kinetics. 

f  He  estimates  that  a  body  falls  in  a  second  a  distance  of  4 
"  bracchia,"  equivalent  to  about  8  feet,  the  true  distance  being 
slightly  over  16. 


176  A  Short  History  of  Astronomy  (Cn.  VI. 

by  its  horizontal  motion,  and  consequently  it  reaches 
the  ground  at  the  same  time  as  a  bullet  simply  allowed 
to  drop;  but  Galilei  gives  no  general  statement  of  this 
principle,  which  was  afterwards  embodied  by  Newton  in 
his  Second  Law  of  Motion. 

The  treatise  on  the  Two  New.  Sciences  was  finished  in 
1636,  and,  since  no  book  of  Galilei's  could  be  printed  in 
Italy,  it  was  published  after  some  little  delay  at  Leyden 
in  1638.  In  the  same  year  his  eyesight,  which  he  had 
to  some  extent  recovered  after  his  first  attack  of  blindness, 
failed  completely,  and  four  years  later  (January  8th,  1642) 
the  end  came. 

134.  Galilei's  chief  scientific  discoveries  have  already 
been  noticed.  The  telescopic  discoveries,  on  which  much 
of  his  popular  reputation  rests,  have  probably  attracted 
more  than  their  fair  share  of  attention ;  many  of  them 
were  made  almost  simultaneously  by  others,  and  the  rest, 
being  almost  inevitable  results  of  the  invention  of  the 
telescope,  could  not  have  been  delayed  long.  But  the 
skilful  use  which  Galilei  made  of  them  as  arguments  for 
the  Coppernican  system,  the  no  less  important  support 
which  his  dynamical  discoveries  gave  to  the  same  cause, 
the  lucidity  and  dialectic  brilliance  with  which  he  marshalled 
the  arguments  in  favour  of  his  views  and  demolished 
those  of  his  opponents,  together  with  the  sensational  in- 
cidents of  his  persecution,  formed  conjointly  a  contribution 
to  the  Coppernican  controversy  which  was  in  effect 
decisive.  Astronomical  text-books  still  continued  to  give 
side  by  side  accounts  of  the  Ptolemaic  and  of  the  Copper- 
nican systems,  and  the  authors,  at  any  rate  if  they  were 
good  Roman  Catholics,  usually  expressed,  in  some  more 
or  less  perfunctory  way,  their  adherence  to  the  former,  but 
there  was  no  real  life  left  in  the  traditional  astronomy; 
new  advances  in  astronomical  theory  were  all  on  Copper- 
nican lines,  and  in  the  extensive  scientific  correspondence 
of  Newton  and  his  contemporaries  the  truth  of  the 
Coppernican  system  scarcely  ever  appears  as  a  subject  for 
discussion. 

Galilei's  dynamical  discoveries,  which  are  only  in  part 
of  astronomical  importance,  are  in  many  respects  his 
most  remarkable  contribution  to  science.  For  whereas  in 


*  134]  Estimate  of  Galilei's   Work  177 

astronomy  he  was  building  on  foundations  laid  by  pre- 
vious generations,  in  dynamics  it  was  no  question  of  im- 
proving or  developing  an  existing  science,  but  of  creating 
a  new  one.  From  his  predecessors  he  inherited  nothing 
but  erroneous  traditions  and  obscure  ideas ;  and  when  these 
had  been  discarded,  he  had  to  arrive  at  clear  fundamental 
notions,  to  devise  experiments  and  make  observations,  to 
interpret  his  experimental  results,  and  to  follow  out  the 
mathematical  consequences  of  the  simple  laws  first  arrived 
a'.  The  positive  results  obtained  may  not  appear  numerous, 
if  viewed  from  the  standpoint  of  our  modern  knowledge, 
but  they  sufficed  to  constitute  a  secure  basis  for  the  super- 
structure which  later  investigators  added. 

It  is  customary  to  associate  with  our  countryman  Francis 
Bacon  (1561-1627)  the  reform  in  methods  of  scientific 
discovery  which  took  place  during  the  seventeenth  century, 
and  to  which  much  of  the  rapid  progress  in  the  natural 
sciences  made  since  that  time  must  be  attributed.  The 
value  of  Bacon's  theory  of  scientific  discovery  is  very 
differently  estimated  by  different  critics,  but  there  can  be 
no  question  of  the  singular  ill-success  which  attended  his 
attempts  to  apply  it  in  particular  cases,  and  it  may  fairly 
be  questioned  whether  the  scientific  methods  constantly 
referred  to  incidentally  by  Galilei,  and  brilliantly  exemplified 
by  his  practice,  do  not  really  contain  a  large  part  of  what 
is  valuable  in  the  Baconian  philosophy  of  science,  while  at 
the  same  time  avoiding  some  of  its  errors.  Reference  has 
already  been  made  on  several  occasions  to  Galilei's  protests 
against  the  current  method  of  dealing  with  scientific 
questions  by  the  interpretation  of  passages  in  Aristotle, 
Ptolemy,  or  other  writers  ;  and  to  his  constant  insistence 
on  the  necessity  of  appealing  directly  to  actual  observation 
of  facts.  But  while  thus  agreeing  with  Bacon  in  these 
essential  points,  he  differed  from  him  in  the  recognition 
of  the  importance,  both  of  deducing  new  results  from 
established  ones  by  mathematical  or  other  processes  of 
exact  reasoning,  and  of  using  such  deductions,  when 
compared  with  fresh  experimental  results,  as  a  means  of 
verifying  hypotheses  provisionally  adopted.  This  method 
of  proof,  which  lies  at  the  base  of  nearly  all  important 
scientific  discovery,  can  hardly  be  described  better  than  by 

12 


178  A  Short  History  of  Astronomy       [CH.  vi.,  $  I34 

Galilei's   own  statement  of  it,  as  applied  to  a   particular 
case : — 

"  Let  us  therefore  take  this  at  present  as  a  Postulatum,  the 
truth  whereof  we  shall  afterwards  find  established,  when  we 
shall  see  other  conclusions  built  upon  this  Hypothesis,  to  answer 
and  most  exactly  to  agree  with  P'xperience."  * 

*   Two  New  Sciences,  translated  by  Weston,  p.  255. 


CHAPTER    VII. 

KEPLER. 

"  His  celebrated  laws  were  the  outcome  of  a  lifetime  of  speculation,, 
for  the  most  part  vain  and  groundless.  .  .  .  But  Kepler's  name  was 
destined  to  be  immortal,  on  account  of  the  patience  with  which  he 
submitted  his  hypotheses  to  comparison  with  observation,  the  candour 
with  which  he  acknowledged  failure  after  failure,  and  the  persever- 
ance and  ingenuity  with  which  he  renewed  his  attack  upon  the 
riddles  of  nature." 

JEVONS. 

135.  JOHN  KEPLER,  or  Keppler,*  was  born  in  1571,  seven 
years  after  Galilei,  at  Weil  in  Wiirtemberg ;  his  parents  were 
in  reduced  circumstances,  though  his  father  had  some  claims 
to  noble  descent.  Though  Weil  itself  was  predominantly 
Roman  Catholic,  the  Keplers  were  Protestants,  a  fact  which 
frequently  stood  in  Kepler's  way  at  various  stages  of  his 
career.  But  the  father  could  have  been  by  no  means 
zealous  in  his  faith,  for  he  enlisted  in  the  army  of  the 
notorious  Duke  of  Alva  when  it  was  engaged  in  trying  to 
suppress  the  revolt  of  the  Netherlands  against  Spanish 
persecution. 

John  Kepler's  childhood  was  marked  by  more  than  the 
usual  number  of  illnesses,  and  his  bodily  weaknesses, 
combined  with  a  promise  of  great  intellectual  ability,  seemed 
to  point  to  the  Church  as  a  suitable  career  for  him.  After 
attending  various  elementary  schools  with  great  irregularity 
— due  partly  to  ill-health,  partly  to  the  requirements  of 

*  The  astronomer  appears  to  have  used  both  spellings  of  his  name 
almost  indifferently.  For  example,  the  title-page  of  his  most 
important  book,  the  Commentaries  on  the  Motions  of  Mars  (§  141), 
qas  the  form  Kepler,  while  the  dedication  of  the  same  book  is  signed 
Kcpplcr. 

179 


180  A  Short  History  of  Astronomy  [CH.  VH. 

manual  work  at  home — he  was  sen":  in  1584  at  the  public 
expense  to  the  monastic  school  at  Adelberg,  and  two  years 
later  to  the  more  advanced  school  or  college  of  the 
same  kind  at  Maulbronn,  which  was  connected  with  the 
University  of  Tubingen,  then  one  of  the  great  centres  of 
Protestant  theology. 

In  1588  he  obta:n'jd  the  B.A.  degree,  and  in  the  following 
year  entered  the  philosophical  faculty  at  Tubingen. 

There  he  came  under  the  influence  of  Maestlin,  the 
professor  of  mathematics,  by  whom  he  was  in  private 
taught  the  principles  of  the  Coppernican  system,  though 
the  professorial  lectures  were  still  on  the  traditional  lines. 

In  1591  Kepler  graduated  as  M.A.,  being  second  out  of 
fourteen  candidates,  and  then  devoted  himself  chiefly  to 
the  study  of  theology. 

136.  In  1594,  however,  the  Protestant  Estates  of  Styria 
applied  to  Tubingen  for  a  lecturer  on  mathematics  (in- 
cluding astronomy)  for  the  high  school  of  Gratz,  and  the 
appointment  was  offered  to  Kepler.  Having  no  special 
knowledge  of  the  subject  and  as  yet  no  taste  for  it,  he 
naturally  hesitated  about  accepting  the  offer,  but  finally 
decided  to  do  so,  expressly  stipulating,  however,  that  he 
should  not  thereby  forfeit  his  claims  to  ecclesiastical 
preferment  in  Wiirtemberg.  The  demand  for  higher 
mathematics  at  Gratz  seems  to  have  been  slight ;  during 
his  first  year  Kepler's  mathematical  lectures  were  attended 
by  very  few  students,  and  in  the  following  year  by  none, 
so  that  to  prevent  his  salary  from  being  wasted  he  was 
set  to  teach  the  elements  of  various  other  subjects.  It 
was  moreover  one  of  his  duties  to  prepare  an  annual 
almanack  or  calendar,  which  was  expected  to  contain  not 
merely  the  usual  elementary  astronomical  information  such 
as  we  are  accustomed  to  in  the  calendars  of  to-day,  but 
also  astrological  information  of  a  more  interesting  character, 
such  as  predictions  of  the  weather  and  of  remarkable  events, 
guidance  as  to  unlucky  and  lucky  times,  and  the  like. 
Kepler's  first  calendar,  for  the  year  1595,  contained  some 
happy  weather-prophecies,  and  he  acquired  accordingly  a 
considerable  popular  reputation  as  a  prophet  and  astrologer, 
which  remained  throughout  his  life. 

Meanwhile  his  official  duties  evidently  left  him  a  good 


5$  136,  137]      Kepler's  Early    Astronomical   }Vork  181 

deal  of  leisure,  which  he  spent  with  characteristic  energy 
in  acquiring  as  thorough  a  knowledge  as  possible  of 
astronomy,  and  in  speculating  on  the  subject. 

According  to  his  own  statement,  "there  were  three 
things  in  particular,  viz.  the  number,  the  size,  and  the 
motion  of  the  heavenly  bodies,  as  to  which  he  searched 
zealously  for  reasons  why  they  were  as  they  were  and  not 
otherwise";  and  the  results  of  a  long  course  of  wild 
speculation  on  the  subject  led  him  at  last  to  a  result  with 
which  he  was  immensely  pleased  —a  numerical  relation 
connecting  the  distances  of  the  several  planets  from  the 
sun  with  certain  geometrical  bodies  known  as  the  regular 
solids  (of  which  the  cube  is  the  best  known),  a  relation 
which  is  not  very  accurate  numerically,  and  is  of  absolutely 
no  significance  or  importance.*  This  discovery,  together 
with  a  detailed  account  of  the  steps  which  led  to  it,  as  well 
as  of  a  number  of  other  steps  which  led  nowhere,  was 
published  in  1596  in  a  book  a  portion  of  the  title  of  which 
may  be  translated  as  The  Forerunner  of  Dissertations  on 
the  Universe,  containing  the  Mystery  of  the  Universe, 
commonly  referred  to  as  the  Mysterium  Cosmtigraphicum. 
The  contents  were  probably  much  more  attractive  and 
seemed  more  valuable  to  Kepler's  contemporaries  than 
to  us,  but  even  to  those  who  were  least  inclined  to  attach 
weight  to  its  conclusions,  the  book  shewed  evidence 
of  considerable  astronomical  knowledge  and  very  gfeat 
ingenuity ;  and  both  Tycho  Brahe  and  Galilei,  to  whom 
copies  were  sent,  recognised  in  the  author  a  rising 
astronomer  likely  to  do  good  work. 

137.  In  1597  Kepler  married.  In  the  following  year  the 
religious  troubles,  which  had  for  some  years  been  steadily 
growing,  were  increased  by  the  action  of  the  Archduke 
Ferdinand  of  Austria  (afterwards  the  Emperor  Ferdinand  II.), 
who  on  his  return  from  a  pilgrimage  to  Loretto  started  a 

*  The  regular  solids  being  taken  in  the  order :  Cube,  tetrahedron, 
dodecahedron,  icosahedron,  octohedron,  and  of  such  magnitude  that 
a  sphere  can  be  circumscribed  to  each  and  at  the  same  time  inscribed 
in  the  preceding  solid  of  the  series,  then  the  radii  of  tie  six  spheres 
so  obtained  were  shewn  by  Kepler  to  be  approximately  proportional 
to  the  distances  from  the  sun  of  the  six  planets  Saturn  Jupiter,  Mars, 
Earth,  Venus,  and  Mercury. 


1 82  A  Short  History  of  Astronomy  [CH.  vn 

* 

vigorous  persecution  of  Protestants  in  his  dominions,  one 
step  in  which  was  an  order  that  all  Protestant  ministers 
and  teachers  in  Styria  should  quit  the  country  at  once 
(1598).  Kepler  accordingly  fled  to  Hungary,  but  returned 
after  a  few  weeks  by  special  permission  of  the  Archduke, 
given  apparently  on  the  advice  of  the  Jesuit  party,  who  had 
hopes  of  converting  the  astronomer.  Kepler's  hearers  had, 
however,  mostly  been  scattered  by  the  persecution,  it  be- 
came difficult  to  ensure  regular  payment  of  his  stipend, 
and  the  rising  tide  of  Catholicism  made  his  position  in- 
creasingly insecure.  Tycho's  overtures  were  accordingly 
welcome,  and  in  1600  he  paid  a  visit  to  him,  as  already 
described  (chapter  v.,  §  108),  at  Benatek  and  Prague.  He 
returned  to  Gratz  in  the  autumn,  still  uncertain  whether  to 
accept  Tycho's  offer  or  not,  but  being  then  definitely 
dismissed  from  his  position  at  Gratz  on  account  of  his 
Protestant  opinions,  he  returned  finally  to  Prague  at  the 
end  of  the  year. 

138.  Soon  after  Tycho's  death  Kepler  was  appointed  his 
successor  as  mathematician  to  the  Emperor  Rudolph  (1602), 
but  at  only  half  his  predecessor's  salary,  and  even  this  w;:s 
paid  with  great  irregularity,  so  that  complaints  as  to  arrears 
and  constant  pecuniary  difficulties  played  an  important  part 
in  his  future  life,  as  they  had  done  during  the  later  years 
at  Gratz.  Tycho's  instruments  never  passed  into  his  pos- 
session, but  as  he  had  little  taste  or  skill  for  observing,  the 
loss  was  probably  not  great ;  fortunately,  after  some  diffi- 
culties with  the  heirs,  he  secured  control  of  the  greater  part 
of  Tycho's  incomparable  series  of  observations,  the  working 
up  of  which  into  an  improved  theory  of  the  solar  system 
was  the  main  occupation  of  the  next  25  years  of  his  life. 
Before,  however,  he  had  achieved  any  substantial  result  in 
this  direction,  he  published  several  minor  works — for  ex- 
ample, two  pamphlets  on  a  new  star  which  appeared  in  1604, 
and  a  treatise  on  the  applications  of  optics  to  astronomy 
(published  in  1604  with  a  title  beginning  Ad  Vitellionem 
Paralipomena  quibus  Astronomiae  Pars  OpticaTraditur  .  .  .), 
the  most  interesting  and  important  part  of  which  was  a 
considerable  improvement  in  the  theory  of  astronomical 
refraction  (chapter  n.,  §46,  and  chapter  v.,  §  no).  A 
later  optical  treatise  (the  Dioptrice  of  1611)  contained  a 


[To  face  p.  183. 


**  138,  i39]          Optical   Work:  Study  of  Mars  183 

suggestion  for  the  construction  of  a  telescope  by  the  use 
of  two  convex  lenses,  which  is  the  form  now  most  commonly 
adopted,  and  is  a  notable  improvement  on  Galilei's  instru- 
ment (chapter  vi.,  §  118),  one  of  the  lenses  of  which  is 
concave ;  but  Kepler  does  not  seem  himself  to  have  had 
enough  mechanical  skill  to  actually  construct  a  telescope 
on  this  plan,  or  to  have  had  access  to  workmen  capable 
of  doing  so  for  him ;  and  it  is  probable  that  Galilei's 
enemy  Scheiner  (chapter  vi.,  §§  124,  125)  was  the  first 
person  to  use  (about  1613)  an  instrument  of  this  kind. 

139.  It  has  already  been  mentioned  (chapter  v.,  §  108) 
that  when  Tycho  was  dividing  the  work  of  his  observatory 
among  his  assistants  he  assigned  to  Kepler  the  study  of 
the  planet  Mars,  probably  as  presenting  more  difficulties 
than  the  subjects  assigned  to  the  others.  It  had  been 
known  since  the  time  of  Coppernicus  that  the  planets, 
including  the  earth,  revolved  round  the  sun  in  paths  that 
were  at  any  rate  not  very  different  from  circles,  and 
that,  the  deviations  from  uniform  circular  motion  could  be 
represented  roughly  by  systems  of  eccentrics  and  epicycles. 
The  deviations  from  uniform  circular  motion  were,  however, 
notably  different  in  amount  in  different  planets,  being, 
for  example,  very  small  in  the  case  of  Venus,  relatively  large 
in  the  case  of  Mars,  and  larger  still  in  that  of  Mercury. 
The  Prussian  Tables  calculated  by  Reinhold  on  a  Copper- 
nican  basis  (chapter  v.,  §  94)  were  soon  found  to  represent 
the  actual  motions  very  imperfectly,  errors  of  4°  and  5° 
having  been  noted  by  Tycho  and  Kepler,  so  that  the 
principles  on  which  the  tables  were  calculated  were  evi- 
dently at  fault. 

The  solution  of  the  problem  was  clearly  more  likely 
to  be  found  by  the  study  of  a  planet  in  which  the  de- 
viations from  circular  motion  were  as  great  as  possible. 
In  the  case  of  Mercury  satisfactory  observations  were 
scarce,  whereas  in  the  case  of  Mars  there  was  an  abundant 
series  recorded  by  Tycho,  and  hence  it  was  true  insight  on 
Tycho's  part  to  assign  to  his  ablest  assistant  this  particular 
planet,  and  on  Kepler's  to  continue  the  research  with  un- 
wearied patience.  The  particular  system  of  epicycles  used 
by  Coppernicus  (chapter  iv.,  §  87)  having  proved  defective, 
Kepler  set  to  work  to  devise  other  geometrical  schemes,  the 


184  A  Short  History  of  Astronomy  [CH.  vn. 

results  of  which  could  be  compared  with  observation.  The 
places  of  Mars  as  seen  on  the  sky  being  a  combined  result 
of  the  motions  of  Mars  and  of  the  earth  in  their  respective 
orbits  round  the  sun,  the  irregularities  of  the  two  orbits 
were  apparently  inextricably  mixed  up,  and  a  great  simpli- 
fication was  accordingly  effected  when  Kepler  succeeded, 
by  an  ingenious  combination  of  observations  taken  at  suit- 
able times,  in  disentangling  the  irregularities  due  to  the 
earth  from  those  due  to  the  motion  of  Mars  itself,  and 
thus  rendering  it  possible  to  concentrate  his  attention  on 
the  latter.  His  fertile  imagination  suggested  hypothesis 
after  hypothesis,  combination  after  combination  of  eccentric, 
epicycle,  and  equant ;  he  calculated  the  results  of  each  and 
compared  them  rigorously  with  observation  ;  and  at  one 
stage  he  arrived  at  a  geometrical  scheme  which  was  capable 
of  representing  the  observations  with  errors  not  exceeding 
8'.*  A  man  of  less  intellectual  honesty,  or  less  convinced 
of  the  necessity  of  subordinating  theory  to  fact  when  the 
two  conflict,  might  have  rested  content  with  this  degree 
of  accuracy,  or  might  have  supposed  Tycho's  refractory 
observations  to  be  in  error.  Kepler,  however,  thought 
otherwise : — 

11  Since  the  divine  goodness  has  given  to  us  in  Tycho  Brahe  a 
most  careful  observer,  from  whose  observations  the  error  of  8' 
is  shewn  in  this  calculation,  ...  it  is  right  that  we  should  with 
gratitude  recognise  and  make  use  of  this  gift  of  God.  .  .  .  For  if 
I  could  have  treated  8'  of  longitude  as  negligible  I  should  have 
already  corrected  sufficiently  the  hypothesis  .  .  .  discovered  in 
chapter  xvi.  But  as  they  could  not  be  neglected,  these  8' 
alone  have  led  the  way  towards  the  complete  reformation  of 
astronomy,  and  have  been  made  the  subject-matter  of  a  great 
part  of  this  work."  f 

140.  He  accordingly  started  afresh,  and  after  trying  a  variety 
of  other  combinations  of  circles  decided  that  the  path  of 
Mars  must  be  an  oval  of  some  kind.  At  first  he  was  in- 
clined to  believe  in  an  egg-shaped  oval,  larger  at  one  end  than 
at  the  other,  but  soon  had  to  abandon  this  idea.  Finally 

*  Two  stars  4'  apart  only  just  appear  distinct  to  the  naked  eye  of 
a  person  with  average  keenness  of  sight. 

|  Commentaries  on  the  Motions  of  Mars,  Part  II.,  end  of  chapter  xix. 


*  MO]    The  Discovery  of  the  Elliptic  Motion  of  Mars      185 

he  tried  the  simplest  known  oval  curvev_the  ellipse,*  and 
found  to  his  delight  that  it  satisfied  the  conditions  of  the 
problem,  if  the  sun  were  taken  to  be  at  a  focus  of  the  ellipse 
described  by  Mars. 

It  was  further  necessary  to  formulate  the  law  of  ^variation 
of  the  rate  of  motion  of  the  planet  in  different  parts  of  its 
orbit.  Here  again  Kepler  tried  a  number  of  hypotheses,  in 
The  course  of  which  he  fairly  lost  his  way  in  the  intricacies 
of  the  mathematical  questions  involved,  but  fortunately 
arrived,  after  a  dubious  process  of  compensation  of  errors, 
at  a  simple  law  which  agreed  with  observation.  He  found 
that  the  planet  moved  fast  when  near  the  sun  and  slowly 
when  distant  from  it,  in  such  a  way  that  the  area  described 
or  swept  out  in  any  time  by  the  line  joining  the  sun  to 
Mars  was  always  proportional  to  the  time.  Thus  in  fig.  6ot 
the  motion  of  Mars  is  most  rapid  at  the  point  A  nearest  to 
the  focus  s  where  the  sun  is,  least  rapid  at  A',  and  the 

*  An  ellipse  is  one  of  several  curves,  known  as  conic  sections, 
which  can  be  formed  by  taking  a  section  of  a  cone,  and  may  also  be 
defined  as  a  curve  the  sum  of  the  distances  of  any  point  on  which 
from  two  fixed  points  inside  it,  known  as  the  foci,  is  always  the  same. 

Thus  if,  in  the  figure,  s  and  H  are  the  foci,  and  P,  Q  are  any  two 


FIG.  59.— An  ellipse. 

points  on  the  curve,  then  the  distances  s  P,  H  P  added  together  are 
equal  to  the  distances  s  Q,  Q  H  added  together,  and  each  sum  is  equal 
to  the  length  A  A'  of  the  ellipse.  The  ratio  of  the  distance  s  H  to 
the  length  A  A'  is  known  as  the  eccentricity,  and  is  a  convenient 
measure  of  the  extent  to  which  the  ellipse  differs  from  a  circle. 

f  The  ellipse  is  more  elongated  than  the  actual  path  of  Mars,  an 
accurate  drawing  of  which  would  be  undistinguishable  to  the  eye 
from  a  circle.  The  eccentricity  is  J  in  the  figure,  that  of  Mars  being  j*-0-. 


1 86  A  Short  History  of  Astronomy  [CH.  vii. 

shaded  and  unshaded  portions  of  the  figure  represent  equal 
areas  each  corresponding  to  the  motion  of  the  planet  during 
a  month.  Kepler's  triumph  at  arriving  at  this  result  is 
expressed  by  the  figure  of  victory  in  the  corner  of  the 
diagram  (fig.  61)  which  was  used  in  establishing  the  last 
stage  of  his  proof. 


FIG.  60. — Kepler's  second  law. 

141.  Thus  were  established  for  the  case  of  Mars  the  two  im- 
portant results  generally  known  as  Kepler's  first  two  laws  : — 

1.  The  planet  describes  an  ellipse,  the  sun  being  in  one  focus. 

2.  The  straight  line  joining  the  planet  to  the  sun  sweeps  out 
equal  areas  in  any  two  equal  intervals  of  time. 

The  full  history  of  this  investigation,  with  the  results 
already  stated  and  a  number  of  developments  and  results 
of  minor  importance,  together  with  innumerable  digressions 
and  quaint  comments  on  the  progress  of  the  inquiry,  was 
published  in  1609  in  a  book  of  considerable  length,  the 
Coinmentaries  on  the  Motions  of  Mars* 
'^142.  Although  the  two  laws  of  planetary  motion  just 
given  were  only  fully  established  for  the  case  of  Mars, 

*  Astronomia  Nova  aiTioXoyrjTOS  sen  Physica  Coelestis,  tradita  Com- 
inentariis  de  Motibus  Stellae  Martis.  Ex  Observationibus  G.  V. 
Tychonis  Brahe. 


141,  142] 


Kepler s  First  and  Second  Laws 


i87 


Kepler  stated  that  the  earth's  path  also  must  be  an  oval 
of  some  kind,  and  was  evidently  already  convinced — aided 
by  his  firm  belief  in  the  harmony  of  Nature — that  all  the 
planets  moved  in  accordance  with  the  same  laws.  This  view 
is  indicated  in  the  dedication  of  the  book  to  the  Emperor 
Rudolph,  which  gives  a  fanciful  account  of  the  work  as  a 


FIG.  61. — Diagram  used  by  Kepler  to  establish  his  laws  of  planetary 
motion.     From  the  Commentaries  on  Mars. 

struggle  against  the  rebellious  War-God  Mars,  as  the  result 
of  which  he  is  finally  brought  captive  to  the  feet  of  the 
Emperor  and  undertakes  to  live  for  the  future  as  a  loyal 
subject.  As,  however,  he  has  many  relations  in  the 
ethereal  spaces— his  father  Jupiter,  his  grandfather  Saturn, 
his  dear  sister  Venus,  his  faithful  brother  Mercury — and  he 
yearns  for  them  and  they  for  him  on  account  of  the  similarity 
of  their  habits,  he  entreats  the  Emperor  to  send  out  an 


1 88  A  Short  History  of  Astronomy  [CH   vu. 

expedition  as  soon  as  possible  to  capture  them  also,  and 
with  that  object  to  provide  Kepler  with  the  "  sinews  of 
war  "  in  order  that  he  may  equip  a  suitable  army. 

Although  the  money  thus  delicately  asked  for  was  only 
supplied  very  irregularly,  Kepler  kept  steadily  in  view  the 
expedition  for  which  it  was  to  be  used,  or,  in  plainer  words, 
he  worked  steadily  at  the  problem  of  extending  his  elliptic 
theory  to  the  other  planets,  and  constructing  the  tables  of 
the  planetary  motions,  based  on  Tycho's  observations,  at 
which  he  had  so  long  been  engaged. 

143.  In  1611  his  patron  Rudolph  was  forced  to  abdicate 
the  imperial  crown  in  favour  of  his  brother  Matthias,  who 
had  little  interest  in  astronomy,  or  even  in  astrology  ;  and 
as  Kepler's  position  was  thus  rendered  more  insecure  than 
ever,  he  opened  negotiations  with   the  Estates  of  Upper 
Austria,   as  the  result  of  which  he  was  promised  a  small 
salary,  on  condition  of  undertaking  the   somewhat  varied 
duties  of  teaching  mathematics  at  the  high  school  of  Linz, 
the  capital,  of  constructing  a  new  map  of  the  province,  and 
of  completing  his  planetary  tables.     For  the  present,  how- 
ever, he  decided  to  stay  with  Rudolph. 

In  the  same  year  Kepler  lost  his  wife,  who  had  long 
been  in  weak  bodily  and  mental  health. 

In  the  following  year  (1612)  Rudolph  died,  and  Kepler 
then  moved  to  Linz  and  took  up  his  new  duties  there, 
though  still  holding  the  appointment  of  mathematician  to 
the  Emperor  and  occasionally  even  receiving  some  portion 
of  the  salary  of  the  office.  In  1613  he  married  again,  after 
a  careful  consideration,  recorded  in  an  extraordinary  but 
very  characteristic  letter  to  one  of  his  friends,  of  the  relative 
merits  of  eleven  ladies  whom  he  regarded  as  possible ;  and 
the  provision  of  a  proper  supply  of  wine  for  his  new  house- 
hold led  to  the  publication  of  a  pamphlet,  of  some  mathe- 
matical interest,  dealing  with  the  proper  way  of  measuring 
the  contents  of  a  cask  with  curved  sides.* 

144.  In  the  years  1618-1621,  although  in  some  ways  the 
most  disturbed  years  of  his  life,  he  published  three  books 
of  importance — an    Epitome  of  the  Copernican  Astronomy, 
the  Harmony  of  the  World^  and  a  treatise  on  Comets. 

*  It  contains  the  germs  of  the  method  of  infinitesimals, 
t  Harmonices  Mundi  Libri  V. 


143,    144] 


Kepler's  Third  Law 


1 89 


The  second  and  most  important  of  these,  published  in 
1619,  though  the  leading  idea  in  it  was  discovered  early 
in  1618,  was  regarded  by  Kepler  as  a  development  of  his 
early  Mysterium  Cosmographicum  (§  136).  His  specula- 
tive and  mystic  temperament  led  him  constantly  to  search 
for  relations  between  the  various  numerical  quantities  occur- 
ring in  the  solar  system  ;  by  a  happy  inspiration  he  thought 
of  trying  to  get  a  relation  connecting  the  sizes  of  the  orbits 
of  the  various  planets  with  their  times  of  revolution  round 
the  sun,  and  after  a  number  of  unsuccessful  attempts  dis- 
covered a  simple  and  important  relation,  commonly  known 
as  Kepler's  third  law  : — 

The  squares  of  the  times  of  revolution  of  any  two  planets 
(including  the  earth)  about  the  sun  are  proportional  to  the 
cubes  of  their  mean  distances  from  the  sun. 

If,  for  example,  we  express  the  times  of  revolution  of 
the  various  planets  in  terms  of  any  one,  which  may  be  con- 
veniently taken  to  be  that  of  the  earth,  namely  a  year,  and  in 
the  same  way  express  the  distances  in  terms  of  the  distance 
of  the  earth  from  the  sun  as  a  unit,  then  the  times  of 
revolution  of  the  several  planets  taken  in  the  order  Mercury, 
Venus,  Earth,  Mars,  Jupiter,  Saturn  are  approximately  '24, 
•615,  i,  r88,  n-86,  29-457,  and  their  distances  from  the 
sun  are  respectively  -387,  723,  i,  1-524,  5-203,  9*539;  if 
now  we  take  the  squares  of  the  first  series  of  numbers  (the 
square  of  a  number  being  the  number  multiplied  by  itself) 
and  the  cubes  of  the  second  series  (the  cube  of  a  number 
being  the  number  multiplied  by  itself  twice,  or  the  square 
multiplied  again  by  the  number),  we  get  the  two  series  of 
numbers  given  approximately  by  the  table  : — 


Mercury. 

Venus. 

Earth. 

Mars. 

Jupiter. 

Saturn. 

Square  of  | 
periodic  V 
time       J 

•058 

•378 

' 

3*54 

140-7 

8677 

Cube     of| 
mean 
distance  J 

•058 

•378 

I 

3'54 

140-8 

867-9 

Here  it  will  be  seen  that  the  two  scries  of  numbers,  in  the 


190  A  Short  History  of  Astronomy  [CH.  vii. 

upper  and  lower  row  respectively,  agree  completely  for  as 
many  decimal  places  as  are  given,  except  in  the  cases  of 
the  two  outer  planets,  where  the  lower  numbers  are  slightly 
in  excess  of  the  upper.  For  this  discrepancy  Newton  after- 
wards assigned  a  reason  (chapter  ix.,  §  186),  but  with  the 
somewhat  imperfect  knowledge  of  the  times  of  revolution 
and  distances  which  Kepler  possessed  the  discrepancy 
was  barely  capable  of  detection,  and  he  was  therefore 
justified  —  from  his  standpoint  —  in  speaking  of  the  law  as 
"precise."* 

It  should  be  noticed  further  that  Kepler's  law  requires 
no  knowledge  of  the  actual  distances  of  the  several  planets 


Saturnus  Jupiter  Mars  fere  Terra 


i! 

Venus     *"•  Mcrcunus  Hie  locum  habeteuanO 

FIG.  62.  —  The  "  music  of  the  spheres,"  according  to  Kepler. 
From  the  Harmony  of  the  World. 

from  the  sun,  but  only  of  their  relative  distances,  i.e.  the 
number  of  times  farther  off  from  the  sun  or  nearer  to  the 
sun  any  planet  is  than  any  other.  In  other  words,  it  is 
necessary  to  have  or  to  be  able  to  construct  a  map  of  the 
solar  system  correct  in  its  proportions^  but  it  is  quite 
unnecessary  for  this  purpose  to  know  the  scale  of  the  map. 

Although  the  Harmony  of  the  World  is  a  large  book, 
there  is  scarcely  anything  of  value  in  it  except  what  has 
already  been  given.  A  good  deal  of  space  is  occupied 
with  repetitions  of  the  earlier  speculations  contained  in  the 

*  There  may  be  some  interest  in  Kepler's  own  statement  of  the 
law:  "Res  est  certissima  exactissimaque,  quod  proportionis  quae 
est  inter  binorum  quorumque  planetarum  tempora  periodica,  sit 
praecise  sesquialtera  proportionis  mediarum  distantiarum,  id  est 
orbium  ipsorum."  —  Harmony  of  the  World,  Book  V.,  chapter  in. 


§i4s]      The  Harmony  of  the   World  and  the  Epitome     191 

Mysterium  Cosmographicum,  and  most  of  the  rest  is  filled 
with  worthless  analogies  between  the  proportions  of  the 
solar— system  and  the  relations  between  various  musical 
scalesT" 

~~  He  is" bold  enough  to  write  down  in  black  and  white  the 
"  music  of  the  spheres  "  (in  the  form  shewn  in  fig.  62),  while 
the  nonsense  which  he  was  capable  of  writing  may  be 
further  illustrated  by  the  remark  which  occurs  in  the  same 
part  of  the  book  :  "  The  Earth  sings  the  notes  M  I,  F  A,  M  I, 
so  that  you  may  guess  from  them  that  in  this  abode  of  ours 
Misery  (miseria)  and  FAmine  (fames)  prevail." 

145.  The  Epitome  of  the  Copernican  Astronomy ',  which 
appeared  in  parts  in  1618,  1620,  and  1621,  although  there 
are  no  very  striking  discoveries  in  it,  is  one  of  the  most 
attractive  of  Kepler's  books,  being  singularly  free  from  the 
extravagances  which  usually  render  his  writings  so  tedious. 
It  contains  within  moderately  short  compass,  in  the  form 
of  question  and  answer,  an  account  of  astronomy  as  known 
at  the  time,  expounded  from  the  Coppernican  standpoint, 
and  embodies  both  Kepler's  own  and  Galilei's  latest  dis- 
coveries. Such  a  text-book  supplied  a  decMed  want,  and 
that  this  was  recognised  by  enemies  as  well  as  by  friends 
was  shewn  by  its  prompt  appearance  in  the  Roman  Index 
of  Prohibited  Books  (cf.  chapter  vi.,  §§  126,  132).  The 
Epitome  contains  the  first  clear  statement  that  the  two 
fundamental  laws  of  planetary  motion  established  for  the 
case  of  Mars  (§  141)  were  true  also  for  the  other  planets 
(no  satisfactory  proof  being,  however,  given),  and  that  they 
applied  also  to  the  motion  of  the  moon  round  the  earth, 
though  in  this  case  there  were  further  irregularities  which 
complicated  matters.  The  theory  of  the  moon  is  worked 
out  in  considerable  detail,  both  evection  (chapter  n.,  §  48) 
and  variation  (chapter  in.,  §  60;  chapter  v.,  §  in)  being 
fully  dealt  with,  though  the  "  annual  equation "  which 
Tycho  had  just  begun  to  recognise  at  the  end  of  his  life 
(chapter  v.,  §  in)  is  not  discussed.  Another  interesting 
development  of  his  own  discoveries  is  the  recognition 
that  his  third  law  of  planetary  motion  applied  also  to 
the  movements  of  the  four  satellites  round  Jupiter,  as 
recorded  by  Galilei  and  Simon  Marius  (chapter  vi.,  §  118). 
Kepler  also  introduced  in  the  Epitome  a  considerable 


192  A  Short  History  of  Astronomy  [Cn.  vii. 

improvement  in  the  customary  estimate  of  the  distance  of 
the  earth  from  the  sun,  from  which  those  of  the  other 
planets  could  at  once  be  deduced. 

If,  as  had  been  generally  believed  since  the  time  of 
Hipparchus  and  Ptolemy,  the  distance  of  the  sun  were 
1,200  times  the  radius  of  the  earth,  then  the  parallax 
(chapter  n.,  §§  43,  49)  of  the  sun  would  at  times  be  as 
much  as  3',  and  that  of  Mars,  which  in  some  positions  is 
much  nearer  to  the  earth,  proportionally  larger.  But  Kepler 
had  been  unable  to  detect  any  parallax  of  Mars,  and  there- 
fore inferred  that  the  distances  of  Mars  and  of  the  sun 
must  be  greater  than  had  been  supposed.  Having  no 
exact  data  to  go  on,  he  produced  out  of  his  imagination 
and  his  ideas  of  the  harmony  of  the  solar  system  a  distance 
about  three  times  as  great  as  the  traditional  one.  He 
argued  that,  as  the  earth  was  the  abode  of  measuring 
creatures,  it  was  reasonable  to  expect  that  the  measurements 
of  the  solar  system  would  bear  some  simple  relation  to  the 
dimensions  of  the  earth.  Accordingly  he  assumed  that 
the  volume  of  the  sun  was  as  many  times  greater  than  the 
volume  of  the  earth  as  the  distance  of  the  sun  was  greater 
than  the  radius  of  the  earth,  and  from  this  quaint  assumption 
deduced  the  value  of  the  distance  already  stated,  which, 
though  an  improvement  on  the  old  value,  was  still  only 
about  one-seventh  of  the  true  distance. 

The  Epitome  contains  also  a  good  account  of  eclipses 
both  of  the  sun  and  moon,  with  the  causes,  means  of 
predicting  them,  etc.  The  faint  light  (usually  reddish)  with 
which  the  face  of  the  eclipsed  moon  often  shines  is  correctly 
explained  as  being  sunlight  which  has  passed  through 
the  atmosphere  of  the  earth,  and  has  there  been  bent  from 
a:  straight  course  so  as  to  reach  the  moon,  which  the  light 
of  the  sun  in  general  is,  owing  to  the  interposition  of  the 
earth,  unable  to  reach.  Kepler  mentions  also  a  ring  of 
light  seen  round  the  eclipsed  sun  in  1567,  when  the 
eclipse  was  probably  total,  not  annular  (chapter  n.,  §  43), 
and  ascribes  it  to  some  sort  of  luminous  atmosphere  round 
the  sun,  referring  to  a  description  in  Plutarch  of  the  same 
appearance.  This  seems  to  have  been  an  early  observation, 
and  a  rational  though  of  course  very  imperfect  explanation, 
of  that  remarkable  solar  envelope  known  as  the  corona 


§  i46]       Kepler  s  Epitome  and  his  Book  on  Comets         193 

which  has  attracted  so  much  attention  in  the  last  half- 
century  (chapter  XIIL,  §  301). 

146.  The  treatise  on  Comets  (1619)  contained  an  account 
of  a  comet  seen  in  1607,  afterwards  famous  as  Halley's 
comet  (chapter  x.,  §  200),  and  of  three  comets  seen  in  1618. 
Following  Tycho,  Kepler  held  firmly  the  view  that  comets 
were  celestial  not  terrestrial  bodies,  and  accounted  for  their 
appearance  and  disappearance  by  supposing  that  they  moved 
in  straight  lines,  and  therefore  after  having  once  passed 
near  the  earth  receded  indefinitely  into  space  ; .  he  does 
not  appear  to  have  made  any  serious  attempt  to  test  this 
theory  by  comparison  with  observation,  being  evidently 
of  opinion  that  the  path  of  a  body  which  would  never 
reappear  was  not  a  suitable  object  for  serious  study.  He 
agreed  with  the  observation  made  by  Fracastor  and  Apian 
(chapter  in.,  §  69)  that  comets'  tails  point  away  from  the 
sun,  and  explained  this  by  the  supposition  that  the  tail  is 
formed  by  rays  of  the  sun  which  penetrate  the  body  of 
the  comet  and  carry  away  with  them  some  portion  of  its 
substance,  a  theory  which,  allowance  being  made  for  the 
change  in  our  views  as  to  the  nature  of  light,  is  a  curiously 
correct  anticipation  of  modern  theories  of  comets'  tails 
(chapter  xm.,  §  304). 

In  a  book  intended  to  have  a  popular  sale '  it  was 
necessary  to  make  the  most  of  the  "  meaning "  of  the 
appearance  of  a  comet,  and  of  its  influence  on  human 
affairs,  and  as  Kepler  was  writing  when  the  Thirty  Years' 
War  had  just  begun,  while  religious  persecutions  and  wars 
had  been  going  on  in  Europe  almost  without  interruption 
during  his  lifetime,  it  was  not  difficult  to  find  sensational 
events  which  had  happened  soon  after  or  shortly  before 
the  appearance  of  the  comets  referred  to.  Kepler  himself 
was  evidently  not  inclined  to  attach  much  importance  to 
such  coincidences  ;  he  thought  that  possibly  actual  contact 
with  a  comet's  tail  might  produce  pestilence,  but  beyond 
that  was  not  prepared  to  do  more  than  endorse  the  pious  if 
somewhat  neutral  opinion  that  one  of  the  uses  of  a  comet  is 
to  remind  us  that  we  are  mortal.  His  belief  that  comets  are 
very  numerous  is  expressed  in  the  curious  form  :  "  There 
are  as  many  arguments  to  prove  the  annual  motion  of  the 
earth  round  the  sun  as  there  are  comets  in  the  heavens." 


194  d  Short  History  of  Astronomy  [Cn.  vil. 

147.  Meanwhile  Kepler's  position  at  Linz  had  become 
more  and  more  uncomfortable,  owing  to  the  rising  tide 
of  the  religious  and  political  disturbances  which  finally 
led  to  the  outbreak  of  the  Thirty  Years'  War  in  1618  ;  but 
notwithstanding  this  he  had  refused  in  1617  an  offer  of 
a  chair  of  mathematics  at  Bologna,  partly  through  attach- 
ment to  his  native  country  and  partly  through  a  well-founded 
distrust  of  the  Papal  party  in  Italy.  Three  years  afterwards 
he  rejected  also  the  overtures  made  by  the  English 
ambassador,  with  a  view  to  securing  him  as  an  ornament 
to  the  court  of  James  I.,  one  of  his  chief  grounds  for  refusal 
in  this  case  being  a  doubt  whether  he  would  not  suffer 
from  being  cooped  up  within  the  limits  of  an  island. 
In  1619  the  Emperor  Matthias  died,  and  was  succeeded 
by  Ferdinand  II.,  who  as  Archduke  had  started  the  perse- 
cution of  the  Protestants  at  Gratz  (§  137)  and  who  had 
few  scientific  interests.  Kepler  was,  however,  after  some 
delay,  confirmed  in  his  appointment  as  Imperial  Mathe- 
matician. In  1620  Linz  was  occupied  by  the  Imperialist 
troops,  and  by  1626  the  oppression  of  the  Protestants  by 
the  Roman  Catholics  had  gone  so  far  that  Kepler  made 
up  his  mind  to  leave,  and,  after  sending  his  family  to 
Regensburg,  went  himself  to  Ulm. 

1 48. 'At  Ulm  Kepler  published  his  last  great  work. 
For  more  than  a  quarter  of  a  century  he  had  been 
steadily  working  out  in  detail,  on  the  basis  of  Tycho's 
observations  and  of  his  own  theories,  the  motions  of  the 
heavenly  bodies,  expressing  the  results  in  such  convenient 
tabular  form  that  the  determination  of  the  place  of  any 
body  at  any  required  time,  as  well  as  the  investigation 
of  other  astronomical  events  such  as  eclipses,  became 
merely  a  matter  of  calculation  according  to  fixed  rules  ; 
this  great  undertaking,  in  some  sense  the  summing  up  of 
his  own  and  of  Tycho's  work,  was  finally  published  in  1627 
as  the  Rudolphine  Tables  (the  name  being  given  in  honour 
of  his  former  patron),  and  remained  for  something  like 
a  century  the  standard  astronomical  tables. 

It  had  long  been  Kepler's  intention,  after  finishing  the 
tables,  to  write  a  complete  treatise  on  astronomy,  to  be 
called  the  New  Almagest;  but  this  scheme  was  never  fairly 
started,  much  less  carried  out. 


$$  147-15°  J  The  Rudolphine  Tables  195 

149.  After  a  number  of  unsuccessful  attempts  to  secure 
the  arrears  of  his  salary,  he  was  told  to  apply  to  Wallenstein, 
the  famous  Imperialist  general,  then  established  in  Silesia 
in  a  semi-independent  position,  who  was  keenly  interested 
in  astrology  and  usually  took  about  with  him  one  or  more 
representatives    of    the    art.      Kepler    accordingly  joined 
Wallenstein  in  1628,  and  did  astrology  for  him,  in  addition 
to  writing  some  minor  astronomical  and  astrological  treatises. 
In  1630  he  travelled  to  Regensburg,  where  the  Diet  was 
then  sitting,  to  press  in  person  his  claims  for  various  arrears 
of  salary ;  but,  worn  out  by  anxiety  and  by  the  fatigues  of 
the  journey,  he  was  seized  by  a  fever  a  few  days  after  his 
arrival,  and  died  on  November  i5th  (N.S.),  1630,  in  his  59th 
year. 

The  inventory  of  his  property,  made  after  his  death, 
shews  that  he  was  in  possession  of  a  substantial  amount, 
so  that  the  effect  of  extreme  poverty  which  his  letters 
convey  must  have  been  to  a  considerable  extent  due  to  his 
over-anxious  and  excitable  temperament. 

150.  In  addition  to  the  great  discoveries  already  men- 
tioned Kepler  made  a  good  many  minor  contributions  to 
astronomy,  such  as  new  methods  of  finding  the  longitude, 
and  various  improvements  in  methods  of  calculation  required 
for  astronomical  problems.     He  also  made  speculations  of 
some  interest  as  to  possible  causes  underlying  the  known 
celestial  motions.     Whereas  the  Ptolemaic  system  required 
a  number  of  motions  round  mere  geometrical  points,  centres 
of  epicycles  or  eccentrics,  equants,  etc.,  unoccupied  by  any 
real  body,  and  many  such  motions  were  still  required  by 
Coppernicus,  Kepler's  scheme  of  the  solar  system  placed  al 
real  body,  the  sun,  at  the  most  important  point  connected  1 
with  the  path  of  each  planet,  and  dealt  similarly  with  the  I 
moon's  motion  round  the  earth  and  with  that  of  the  four 
satellites   round  Jupiter.      Motions  of  revolution  came  in 
fact  to  be  associated  not  with  some  central  point  but  with 
some  central  body,  and  it  became  therefore  an  inquiry  of 
interest  to  ascertain  if  there  were  any  connection  between 
the  motion  and  the  central  body.     The  property  possessed 
by  a  magnet  of  attracting  a  piece  of  iron  at  some  little 
distance  from  it  suggested  a  possible  analogy  to  Kepler, 
who  had  read  with  care  and  was  evidently  impressed  by 


196 


A  Short  History  of  Astronomy 


[CH.   VII. 


the  treatise  On  the  Magnet  (De  Magnete)  published  in 
1600  by  our  countryman  William  Gilbert  of  Colchester 
(1540-1603).  He  suggested  that  the  planets  might  thus 
be  regarded  as  connected  with  the  sun,  and  therefore  as 
sharing  to  some  extent  the  sun's  own  motion  of  revolution. 
In  other  words,  a  certain  "  carrying  virtue "  spread  out 
from  the  sun,  with  or  like  the  rays  of  light  and  heat,  and 
tried  to  carry  the  planets  round  with  the  sun. 

"  There  is  there- 
fore a  conflict  be- 
tween the  carrying 
power  of  the  sun  and 
the  impotence  or 
material  sluggishness 
(inertia)  of  the 
planet;  each  enjoys 
some  measure  of 
victory,  for  the  former 
moves  the  planet 
from  its  position  and 
the  latter  frees  the 
planet's  body  to  some 
extent  from  the  bonds 
in  which  it  is  thus 
held,  .  .  .  but  only  to 
be  captured  again  by 
another  portion  of 
this  rotatory  virtue."  * 


FIG.  63. — Kepler's  idea  of  gravity. 
From  the  Epitome. 


The  annexed 
diagram  is  given 
by  Kepler  in  illustration  of  this  rather  confused  and  vague 
theory. 

He  believed  also  in  a  more  general  "  gravity,"  which  he 
defined  f  as  "  a  mutual  bodily  affection  between  allied  bodies 
tending  towards  their  union  or  junction,"  and  regarded  the 
tides  as  due  to  an  action  of  this  sort  between  the  moon  and 
the  water  of  the  earth.  But  the  speculative  ideas  thus 
thrown  out,  which  it  is  possible  to  regard  as  anticipations 
of  Newton's  discovery  of  universal  gravitation,  were  not  in 
any  way  developed  logically,  and  Kepler's  mechanical  ideas 


*  Epitome,  Book  IV.,  Part  2. 

f  Introduction  to  the  Commentaries  on  the  Motions  of  Mars. 


*  isO  Estimate  of  Kepler's   Work  197 

were  too  imperfect  for  him  to  have  made  real  progress  in 
this  direction. 

151.  There  are  few  astronomers  about  whose  merits  such 
different  opinions  have  been  held  as  about  Kepler.  There 
is,  it  is  true,  a  general  agreement  as  to  the  great  import- 
ance of  his  three  laws  of  planetary  motion,  and  as  to  the 
substantial  value  of  the  Rudolphine  Tables  and  of  various 
minor  discoveries.  These  results,  however,  fill  but  a  small 
part  of  Kepler's  voluminous  writings,  which  are  encumbered 
with  masses  of  wild  speculation,  of  mystic  and  occult 
fancies,  of  astrology,  weather  prophecies,  and  the  like,  which 
are  not  only  worthless  from  the  standpoint  of  modern 
astronomy,  but  which — unlike  many  erroneous  or  imperfect 
speculations — in  no  way  pointed  towards  the  direction  in 
which  the  science  was  next  to  make  progress,  and  must 
have  appeared  almost  as  unsound  to  sober-minded  con- 
temporaries like  Galilei  as  to  us.  Hence  as  one  reads 
chapter  after  chapter  without  a  lucid  still  less  a  correct  idea, 
it  is  impossible  to  refrain  from  regrets  that  the  intelligence 
of  Kepler  should  have  been  so  wasted,  and  it  is  difficult 
not  to  suspect  at  times  that  some  of  the  valuable  results 
which  lie  imbedded  in  this  great  mass  of  tedious  specula- 
tion were  arrived  at  by  a  mere  accident.  On  the  other 
hand,  it  must  not  be  forgotten  that  such  accidents  have  a 
habit  of  happening  only  to  great  men,  and  that  if  Kepler 
loved  to  give  reins  to  his  imagination  he  was  equally  im- 
pressed with  the  necessity  of  scrupulously  comparing 
speculative  results  with  observed  facts,  and  of  surrendering 
without  demur  the  most  beloved  of  his  fancies  if  it  was 
unable  to  stand  this  test.  If  Kepler  had  burnt  three- 
quarters  of  what  he  printed,  we  should  in  all  probability 
have  formed  a  higher  opinion  of  his  intellectual  grasp  and 
sobriety  of  judgment,  but  we  should  have  lost  to  a  great 
extent  the  impression  of  extraordinary  enthusiasm  and 
industry,  and  of  almost  unequalled  intellectual  honesty, 
which  we  now  get  from  a  study  of  his  works. 


CHAPTER  VIII. 

FROM    GALILEI    TO    NEWTON. 

".Andgnow|thc  lefty  telescope,  the  scale 
By  which  they  venture  heaven  itself  t'assail, 
Was  raised,  and  planted  full  against  the  moon." 

Hudibras 

152.  BETWEEN  the  publication  of  Galilei's  Two  New 
Sciences  (1638)  and  that  of  Newton's  Principia  (1687)  a 
period  of  not  quite  half  a  century  elapsed ;  during  this 
interval  no  astronomical  discovery  of  first-rate  importance 
was  published,  but  steady  progress  was  made  on  lines 
already  laid  down. 

On  the  one  hand,  while  the  impetus  given  to  exact  observa- 
tion by  Tycho  Brahe  had  not  yet  spent  itself,  the  invention 
of  the  telescope  and  its  gradual  improvement  opened  out  an 
almost  indefinite  field  for  possible  discovery  of  new  celestial 
objects  of  interest.  On  the  other  hand,  the  remarkable 
character  of  the  three  laws  in  which  Kepler  had  summed 
up  the  leading  characteristics  of  the  planetary  motions 
could  hardly  fail  to  suggest  to  any  intelligent  astronomer 
the  question  why  these  particular  laws  should  hold,  or,  in 
other  words,  to  stimulate  the  inquiry  into  the  possibility  of 
shewing  them  to  be  necessary  consequences  of  some 
simpler  and  more  fundamental  law  or  laws,  while  Galilei's 
researches  into  the  laws  of  motion  suggested  the  possibility 
of  establishing  some  connection  between  the  causes  under- 
lying these  celestial*  motions  and  those  of  ordinary  terrestrial 
objects. 

153.  It  has  been  already  mentioned  how  closely  Galilei 
was  followed  by  other  astronomers  (if  not  in  some  cases 
actually  anticipated)  in  most  of  his  telescopic  discoveries. 

198 


CH.  viii.,  «§  152— 154]       Telescopic  Discoveries  199 

To  his  rival  Christopher  Scheiner  (chapter  vi.,  §§  124,  125) 
belongs  the  credit  of  the  discovery  of  bright  cloud-like 
objects  on  the  sun,  chiefly  visible  near  its  edge,  and  from 
their  brilliancy  named  faculae  (little  torches).  Scheiner  made 
also  a  very  extensive  series  of  observations  of  the  motions 
and  appearances  of  spots. 

The  study  of  the  surface  of  the  moon  was  carried  on 
with  great  care  by  John  Hevel  of  Danzig  (1611-1687),  who 
published  in  1647  jus  ^eienn^ynp^^r^r  description  of  the 
moon,  magnificently  illustrated  by  plates  engraved  as  well 
as  drawn  by  himself.  The  chief  features  of  the  moon — 
mountains,  craters,  and  the  dark  spaces  then  believed  to  be 
seas — were  systematically  described  and  named,  for  the 
most  p.irt  after  corresponding  features  of  our  own  earth. 
Revel's  names  for  the  qhief  mountain  ranges,  e.g.  the 
Apennines  and  the  Alps,  and  for  the  seas,  e.g.  Mare 
Serenitatis  or  Pacific  Ocean,  have  lasted  till  to-day;  but 
similar  names  given  by  him  to  single  mountains  and  craters 
have  disappeared,  and  they  are  now  called  after  various 
distinguished  men  of  science  and  philosophers,  e.g.  Plato 
and  Coppernicus,  in  accordance  with  a  system  introduced 
by  John  Baptist  Ric^ioli  (1598-1671)  in  his  bulky  treatise 
on  astronomy  called  the  New  Almagest  (165 1). 

Hevelt  who  gasman  indefatigable  worker,  published  two 
large  books  on  comets,  Prodromus  Cometicus  (1654)  and 
Cometographia(i66&),  containing  the  first  systematic  account 
of  all  recorded  comets.  He  constructed  also  a  catalogue 
of  about  1,500  stars,  observed  on  the  whole  with  accuracy 
rather  greater  than  Tycho's,  though  still  without  the  use  of 
the  telescope ;  he  published  in  addition  an  improved  set 
of  tables  of  the  sun,  and  a  variety  of  other  calculations  and 
observations. 

154.  The  planets  were  also  watched  with  interest  by  a 
number  of  observers,  who  detected  at  different  times  bright 
or  dark  markings  on  Jupiter,  Mars,  and  Venus.  The  two 
appendages  of  Saturn  which  Galilei  had  discovered  in  1610 
and  had  been  unable  to  see  two  years  later  (chapter  vi.,  §  123) 
were  seen  and  described  by  a  number  of  astronomers 
under  a  perplexing  variety  of  appearances,  and  the  mystery 
was  only  unravelled,  nearly  half  a  century  after  Galilei's  first 
observation,  by  the  greatest  astronomer  of  this  period, 


2oo  A  Short  History  of  Astronomy     [CH.  vin.,  $  154 

iQhristiaan  Huygenp  (1629-1695),  a  native  of  the  Hague. 
Huygens  possessed  remarkable  ability,  both  practical  and 
theoretical,  in  several  different  directions,  and  his  contribu- 
tions to  astronomy  were  only  a  small  part  of  his  services 
to  science.  Having  acquired  the  art  of  grinding  lenses 
with  unusual  accuracy,  he  was  able  to  construct  telescopes 
I  of  much  greater  power  than  his  predecessors.  By  the  help  of 
[one  of  these  instruments  he  discovered  in  i_65j  a  satellite  of 
Saturn  (Titan).  With  one  of  those  remnants  of  mediaeval 
mysticism  from  which  even  the  soberest  minds  of  the  century 
freed  themselves  with  the  greatest  difficulty,  he  asserted  that, 
as  the  total  number  of  planets  and  satellites  now  reached  the 
perfect  number  12,  no  more  remained  to  be  discovered — a 
prophecy  which  has  been  abundantly  falsified  since  (§  160; 
chapter  XIL,  §§  253,  255  ;  chapter  xin.,  §§  289,  294,  295). 
Using  a  still  finer  telescope,  and  aided  by  his  acuteness 

rin  interpreting  his  observations,  Huygens  made  the  much 
more  interesting  discovery  that  the  puzzling  appearances 
seen  round  Saturn  were  due  to  a  thin  ring  (fig.  64)  inclined  at 
a  considerable  angle  (estimated  by  him  at  31°)  to  the  plane 
of  the  ecliptic,  and  therefore  also  to  the  plane  in  which 
Saturn's  path  round  the  sun  lies.  This  result  was  first 
announced — according  to  the  curious  custom  of  the  time — 
by  an  anagram,  in  the  same  pamphlet  in  which  the  dis- 
covery of  the  satellite  was  published,  De  Saturni  Luna 
Observatio  Nova  (1656);  and  three  years  afterwards  (1659) 
the  larger  Systema  Saturnium  appeared,  in  which  the  in- 
terpretation of  the  anagram  was  given,  and  the  varying 
appearances  seen  both  by  himself  and  by  earlier  observers 
were  explained  with  admirable  lucidity  and  thoroughness. 
The  ring  being  extremely  thin  is  invisible  either  when 
its  edge  is  presented  to  the  observer  or  when  it  is  pre- 
sented to  the  sun,  because  in  the  latter  position  the  rest 
of  the  ring  catches  no  light.  Twice  in  the  course  of 
Saturn's  revolution  round  the  sun  (at  B  and  D  in  fig.  66), 
i.e.  at  intervals  of  about  15  years,  the  plane  of  the  ring 
passes  for  a  short  time  through  or  very  close  both  to  the 
earth  and  to  the  sun,  and  at  these  two  periods  the  ring  is 
consequently  invisible  (fig.  65).  Near  these  positions  (as  at 
Q,  R,  s,  T)  the  ring  appears  much  foreshortened,  and  pre- 
sents the  appearance  of  two  arms  projecting  from  the  body 


FIG.  64. — Saturn's  ring,  as  drawn  by  Huygens.     From  the 
Systenia  Saiiiruititn. 


FIG.  65. — Saturn,  with  the  ring  seen  edge-wise.     From  the 

Sy sterna  Saturnium.  [To  face  p.  200 


202  A  Short  History  of  Asironcmy          [CH.  vm. 

of  Saturn;  farther  off  still  the  ring  appeals  wider  and  the 
opening  becomes  visible;  and  about  seven  years  before 
and  after  i  the  periods  of  invisibility  (at  A  and  c)  the  ring 
is  seen  at  its  widest.  Huygens  gives  for  comparison  with 
his  own  results  a  number  of  drawings  by  earlier  observers 
(reproduced  in  fig.  67),  from  which  it  may  be  seen  how 
near  son  e  of  them  were  to  the  discovery  of  the  ring. 

155.  To  our  countryman  William  Gqs&ig&e  (  1  6  1  2  ?-i  644) 
j  is  due  the  first  recognition  that  the  telescopecouM  be  utilised, 
1  not  merely  for  observing  generally  the  appearances  of  celestial 
J  bodies,  but  also  as  an  instrument  of  precision,  which  would 

give  the  directions  of  stars,  etc.,  with  greater  accuracy  than 
is  possible  with  the  naked  eye,  and  would  magnify  small 
angles  in  such  a  way  as  to  facilitate  the  measurement 
of  angular  distances  between  neighbouring  stars,  of  the 
diameters  of  the  planets,  and  of  similar  quantities.  He  was 
unhappily  killed  when  quite  a  young  man  at  the  battle 
of  Marston  Moor  (1644),  but  his  letters,  published  many 
years  afterwards  shew  that  by  1640  he  was  familiar  with 
the  use  of  telescopic  "  sights,"  for  determining  with 
/  accuracy  the  position  of  a  star,  and  that  he  had  constructed 
/  a  so-called  micrometer*  with  which  he  was  able  to  measure 
I  angles  of  a  few  seconds.  Nothing  was  known  of  his  dis- 
coveries at  the  time,  and  it  was  left  for  Huygens  to  invent 
independently  a  micrometer  of  an  inferior  kind  (1658),  and 
for  Adrien  Auzout  (?—  1691)  to  introduce  as  an  improvement 
(about  1666)  an  instrument  almost  identical  with  Gascoigne's. 

I  The  systematic  use  of  telescopic  sights  for  the  regular 
work  of  an  observatory  was  first  introduced  about  1667  by 
Auzout's  friend  and  colleague  Jean  Picard  (1620-1682). 

156.  With   Gascoigne  should   be    mentioned   his  friend 

(  T  ^  T  y  ?_i64i),  who  was  an  enthusiastic 


admirer  of  Kepler  and  had  made  a  considerable  improve- 
ment in  the  theory  of  the  moon,  by  taking  the  elliptic  orbit 
as  a  basis  and  then  allowing  for  various  irregularities.  He 
was  the  first  observer  of  a  transit  of  Venus,  i.e.  a  passage 
of  Venus  over  the  disc  of  the  sun,  an  event  which  took 
place  in  1639,  contrary  to  the  prediction  of  Kepler  in  the 
Rudolphine  Tables^  but  in  accordance  with  the  rival  tables 

*  Substantially  the  /Air  micrometer  of  modern  astronomy 


FIG.  67. — Earlv  drawings  of  Saturn. 


From"  the  Sy sterna  Saturnium. 

[.To  face  p.  202. 


v$  155—158]  Gascoigtte)  llorrocks,  liny  gens  203 

of  Philips  von  Lansberg  (1561-1632),  \vhicii  Burrocks  had 
verified  for  the  purpose.  It  was  not,  however,  till  long 
afterwards  that  Halley  pointed  out  the  importance  of  the 
transit  of  Venus  as  a  means  of  ascertaining  the  distance  of 
the  sun  from  the  earth  (chapter  x.,  §  202).  It  is  also  worth 
noticing  that  Horrocks  suggested  the  possibility  of  the 
irregularities  of  the  moon's  motion  being  due  to  the  disturb- 
ing action  of  the  sun,  and  that  he  also  had  some  idea  of 
certain  irregularities  in  the  motion  of  Jupiter  and  Saturn, 
now  known  to  be  due  to  their  mutual  attraction  (chap'.er  x., 
§  204  ;  chapter  XL,  §  243). 

157.  Another  of  Huygens's  discoveries  revolutionised  the 
art  of  exact  astronomical  observation.     This  was  the  inven- 
tion of  the  pendulum-clock  (made  1656,  patented  in  1657). 
It  has   bee fT already  'mentioned  how  the   same   discovery 
was  made  by  Biirgi,  but  virtually  lost  (see  chapter  v.,  §  98) ; 
and  how  Galilei  again  introduced  the  pendulum  as  a  time- 
measurer  (chapter  vi.,  §  114).    Galilei's  pendulum,  however, 
could  only  be  used  for  measuring  very  short  times,  as  there 
was  no  mechanism  to  keep  it  in  motion,  and  the  motion 
soon  died  away.     Huygens  attached  a  pendulum  to  a  clock 
driven  by  weights,  so  that  the  clock  kept  the  pendulum  going 
and  the  pendulum   regulated   the  clock.*     Henceforward 
it   was  possible  to  take  reasonably  accurate  time-observa- 
tions, and,  by  noticing  the  interval  between  the   passage 
of  two  stars  across  the  meridian,  to  deduce,  from  the  known 
rate  of  motion  of  the  celestial  sphere,  their  angular  distance 
east  and  west  of  one  anoth'er,  thus  helping  to  fix  the  position 
of  one  with  respect  to  the  other.   It  was  again  Picard  (§  155) 
who  first  recognised  the  astronomical  importance  of  this 
discovery,  and  introduced  regular  time-observations  at  the 
new  Observatory  of  Paris. 

158.  Huygens  was  not  content  with   this   practical   use 
of  the   pendulum,  but  worked  out  in   his   treatise  called 
Oscillator ium  Horologium  or  The  Pendulum  Clock  (1673)  a 
number  of  important  results  in  the  theory  of  the  pendulum, 
and  in  the  allied  problems  connected  with  the  motion  of 
a  body  in  a  circle  or  other  curve.    The  greater  part  of  these 

*  Galilei,  at  the  end  of  his  life,  appears  to  have  thought  of  contriving 
a  pendulum  with  clockwork,  but  there  is  no  satisfactory  evidence  that 
he  ever  carried  out  the  idea. 


264  A  Short  History  of  Astronomy  [CH.  vin. 

investigations  lie  outside  the  field  of  astronomy,  but  his 
formula  connecting  the  time  of  oscillation  of  a  pendulum 
with  its  length  and  the  intensity  of  gravity  *  (or,  in  other 
words,  the  rate  of  falling  of  a  heavy  body)  afforded  a  prac- 
tical means  of  measuring  gravity,  of  far  greater  accuracy 
than  any  direct  experiments  on  falling  bodies ;  and  his 
study  of  circular  motion,  leading  to  the  result  that  a  body 
moving  in  a  circle  must  be  acted  on  by  some  force  towards 
the  centre,  the  magnitude  of  which  depended  in  a  definite 
way  on  the  speed  of  the  body  and  the  size  of  the  circle,t  is 
of  fundamental  importance  in  accounting  for  the  planetary 
motions  by  gravitation. 

159.  During  the  iyth  century  also  the  first  measurements 
of  the  earth  were  made  which  were  a  definite  advance  on 
those   of  the   Greeks   and   Arabs  (chapter  n.,  §§  36,  45, 
and  chapter  in.,  §  57).      Willebrord  Snell  (1591-1626),  best 
known  by  his  discovery  of  the  law  of  refraction  of  light, 
made  a  series  of  measurements  in  Holland  in  1617,  from 
which  the  length  of  a  degree  of  a  meridian  appeared  to  be 
about  67  miles,  an  estimate  subsequently  altered  to  about 
69  miles  by  one  of  his  pupils,  who  corrected  some  errors 
in  the  calculations,  the   result   being   then  within   a   few 
hundred  feet  of  the  value  now  accepted.     Next,  Richard 
Norwood '(1590  ?-i6'75)  measured  the  distance  from  London 
tc  York,  and  hence   obtained   (1636)  the   length   of  the 
degree   with  .an   error   of  less  than   half  a  mile.     Lastly, 
Picard  in  1671    executed  some  .measurements  .near  Paris 
leading  to  a  result  only  a  few  yards  wrong.     The  length 
of  a  degree  being  known,  the  circumference  and  radius  of 
the  earth  can  at  once  be  deduced. 

1 60.  Auzout  and  Picard  were  two  members  of  a  group 
of  observational  astronomers  working  at  Paris,  of  whom  the 
best  known,  though  probably  not  really  the  greatest,  was 
Giovanni   Domenico    Cassini    (1625-1712).     Born   in   the 
north  of  Italy,  he  acquired  a  great  reputation,  partly  by 
some  rather   fantastic    schemes    for    the   construction   of 
gigantic  instruments,  partly  by  the  discovery  of  the  rotation 

*  In  modern  notation:  time  of  oscillation  =  2 TT V/^. 
f  I.e.  he  obtained  the  familiar  formula  v^/r,  and  several  equivalent 
forms  for  centrifugal  force. 


$§  159-161]     Measurements  of  the  Earth :  Cassini  205 

of  Jupiter  (1665),  of  Mars  (1666),  and  possibly  of  Venus 
(1667),  and  also  by  his  tables  of  the  motions  of  Jupiter's 
moons  (1668).  The  last  caused  Picard  to  procure  for  him 
an  invitation  from  Louis  XIV.  (1669)  to  come  to  Paris 
and  to  exercise  a  general  superintendence  over  the  Obser- 
vatory, which  was  then  being  built  and  was  substantially 
completed  in  1671.  Cassini  was  an  industrious  observer 
and  a  voluminous  writer,  with  a  remarkable  talent  for 
impressing  the  scientific  public  as  well  as  the  Court.  He 
possessed  a  strong  sense  of  the  importance  both  of  himself 
and  of  his  work,  but  it  is  more  than  doubtful  if  he  had  as 
clear  ideas  as  Picard  of  the  really  important  pieces  of  work 
which  ought  to  be  done  at  a  public  observatory,  and  of 
the  way  to  set  about  them.  But,  notwithstanding  these 
defects,  he  rendered  valuable  services  to  various  departments 
of  astronomy.  He  discovered  four  new  satellites  of  Saturn  : 
Japetus  in  1671,  Rhea  in  the  following  year,  Dione  and 
Thetis  in  1684  ;  and  also  noticed  in  1675  a  dark  marking 
in  Saturn's  ring,  which  has  subsequently  been  more  dis- 
tinctly recognised  as  a  division  of  the  ring  into  two,  an 
inner  and  an  outer,  and  is  known  as  Cassini's  division 
(see  fig.  95  facing  p.  384).  He  also  improved  to  some 
extent  the  theory  of  the  sun,  calculated  a  fresh  table  of 
atmospheric  refraction  which  was  an  improvement  on 
Kepler's  (chapter  vii.,  §  138),  and  issued  in  1693  a  fresn  set 
of  tables  of  Jupiter's  moons,  which  were  much  more  accurate 
than  those  which  he  had  published  in  1668,  and  much  the 
best  existing. 

161.  It  was  probably  at  the  suggestion  of  Picard  or  Cassini 
that  one  of  their  fellow  astronomers,  John  Richer  (?-i6Q6), 
otherwise  almost  unknown,  undertook ^107 1-3)  a  scientinc 
expedition  to  Cayenne  (in  latitude  5°  N.).     Two  important 
results  were  obtained.     It  was  found  that  a  pendulum  of 
given  length  beat  more  slowly  at  Cayenne  than  at  Paris, 
thus  shewing  that  the  intensity  of  gravity  was  less  near  the 
equator  than  in  higher  latitudes.    This  fact  suggested  that  the 
earth  was  not  a  perfect  sphere,  and  was  afterwards  used  in  ; 
connection  with  theoretical  investigations  of  the  problem  of  j 
the  earth's  shape  (cf.  chapter  ix.,  §  187).     Again,  Richer's  { 
observations  of  the  position  of  Mars  in  the  sky,  combined  I 
with  observations  taken  at  the  same  time  by  Cassini,  Picard,  \ 


206 


A  Short  History  of  Astronomy 


[Cu.  VIII. 


M 


and  others  in  France,  led  to  a  reasonably  accurate  estimate 
of  the  distance  of  Mars  and  hence  of  that  of  the  sun. 
Mars  was  at  the  time  in  opposition  (chapter  n.,  §  43),  so 

that  it  was  nearer  to  the  earth 
than  at  other  times  (as  shewn 
in  fig.  68),  and  therefore 
favourably  situated  for  such 
observations.  The  principle 
of  the  method  is  extremely 
simple  and  substantially  iden- 
tical with  that  long  used  in 
the  case  of  the  moon  (chap- 
ter IL,  §  49).  One  observer 
is,  say,  at  Paris  (P,  in  fig.  69), 
and  observes  the  direction  in 
which  Mars  appears,  i.e.  the 
direction  of  the  line  P  M  ;  the 
other  at  Cayenne  (c)  observes  similarly  the  direction  of 
the  line  c  M.  The  line  c  P,  joining  Paris  and  Cayenne,  is 
known  geographically ;  the  shape  of  the  triangle  c  P  M  and 


FIG.  68. — Mars  in  opposition. 


FIG.  69. — The  parallax  of  a  planet. 

the   length   of  one   of  its   sides    being    thus   known,    the 
lengtns  of  the  other  sides  are   readily  calculated. 

The  result  of  an  investigation  of  this  sort  is  often  most 
conveniently  expressed  by  means  of  a  certain  angle,  from 


$  x6x]  Parallax  207 

whic'j  the  distance  in  terms  of  the  radius  of  the  earth,  and 
hence  in  miles,  can  readily  b*  deiuced  when  desired. 

The  parallax  of  a  heavenly  bo_ly  such  as  the  moon,  the 
sun,  or  a  planet,  being  in  the  first  instance  defined  generally 
(chapter  IL,  §  43)  as  the  angb  (o  M  p)  between  the  lines 
joining  the  heavenly  body  to  the  observer  and  to  the 
centre  of  the  earth,  varies  in  general  with  the  position  of 
the  observer.  It  is  evidently  greatest  when  the  observer 
is  in  such  a  position,  as  at  Q,  that  the  line  M  Q  touches  the 
earth ;  in  this  position  M  is  on  the  observer's  horizon. 
Moreover  the  angle  o  Q  M  being  a  right  angle,  the  shape 
of  the  triangle  and  the  ratio  of  its  sides  are  completely 
known  when  the  angle  o  M  Q  is  known.  Since  this  angle 
is  the  parallax  of  M,  when  on  the  observer's  horizon,  it  is 
called  the  horizontal  parallax  of  M,  but  the  word  horizontal 
is  frequently  omitted.  It  is  easily  seen  by  a  figure  that 
the  more  distant  a  body  is  the  smaller  is  its  horizontal 
parallax ;  and  with  the  small  parallaxes  with  which  we  are 
concerned  in  astronomy,  the  distance  and  the  horizontal 
parallax  can  be  treated  as  inversely  proportional  to  one 
another ;  so  that  if,  for  example,  one  body  is  twice  as 
distant  as  another,  its  parallax  is  half  as  great,  and  so  on.  . 

It  may  be  convenient  to  point  out  here  that  the  word 
"parallax"  is  used  in  a  different  though  analogous  sense  when 
a  fixed  star  is  in  question.  The  apparent  displacement 
of  a  fixed  star  due  to  the  earth's  motion  (chapter  iv.,  §  92), 
which  was  not  actually  detected  till  long  afterwards 
(chapter  XIIL,  §  278),  is  called  annual  or  stellar  parallax 
(the  adjective  being  frequently  omitted) ;  and  the  name 
is  applied  in  particular  to  the  greatest  angle  between  the 
direction  of  the  star  as  seen  from  the  sun  and  as  seen  from 
the  earth  in  the  course  of  the  year.  If  in  fig.  69  we  regard 
M  as  representing  a  star,  o  the  sun,  and  the  circle  as  being 
the  earth's  path  round  the  sun,  then  the  angle  OMQ'is  the 
annual  parallax  of  M. 

In  this  particular  case  Cassini  deduced  from  Richer's 
observations,  by  some  rather  doubtful  processes,  that  the 
sun's  parallax  was  about  9" -5,  corresponding  to  a  distance 
from  the  earth  of  about  87,000,000  miles,  or  about  360 
times  the  distance  of  the  moon,  the  most  probable  value, 
according  to  modern  estimates  (chapter  XIIL,  §  284),  being 


208  A  Short  History  of  Astronomy  [Cn.  vm. 

a  little  less  than  93,000,000.  Though  not  really  an  accurate 
result,  this  was  an  enormous  improvement  on  anything 
that  had  gone  before,  as  Ptolemy's  estimate  of  the  sun's 
distance,  corresponding  to  a  parallax  of  3',  had  survived 
up  to  the  earlier  part  of  the  iyth  century,  and  although 
it  was  generally  believed  to  be  seriously  wrong,  most 
corrections  of  it  had  been  purely  conjectural  (chapter  vn., 

§§  MS)- 

162.  Another  famous  discovery  associated  with  the  early 
days    of  the    Paris  Observatory  was  that  of  the  velocity 
of  light.      In    1671    Picard  paid  a  visit   to  Denmark   to 
examine  what  was  left  of  Tycho    Brahe's   observatory  at 
Hveen,   and   brought   back   a  young   Danish    astronomer, 
Olaus  Roemer  (1644-1710),  to  help  him  at  Paris.     Roemer, 
in  studying  the  motion  of  Jupiter's  moons,  observed  (1675) 
that  the  intervals  between  successive  eclipses  of  a  moon 
(the  eclipse  being  caused  by  the  passage  of  the  moon  into 
Jupiter's  shadow)  were  regularly  less  when  Jupiter  and  the 
earth  were  approaching  one  another  than  when  they  were 

j  receding.  This  he  saw  to  be  readily  explained  by  the 
!  supposition  that  light  travels  through  space  at  a  definite 
j  though  very  great  speed.  Thus  if  Jupiter  is  approaching 
the  earth,  the  time  which  the  light  from  one  of  his  moons 
takes  to  reach  the  earth  is  gradually  decreasing,  and  con- 
sequently the  interval  between  successive  eclipses  as  seen 
by  us  is  apparently  diminished.  From  the  difference  of 
the  intervals  thus  observed  and  the  known  rates  of  motion 
of  Jupiter  and  of  the  earth,  it  was  thus  possible  to  form  a 
rough  estimate  of  the  rate  at  which  light  travels.  Roemer 
also  made  a  number  of  instrumental  improvements  of 
importance,  but  they  are  of  too  technical  a  character  to 
be  discussed  here. 

163.  One  great  name  belonging  to  the  period  dealt  with 
in  this  chapter   remains    to   be   mentioned,  that   of  Rene 
Descartes*  (1596-1650).     Although  he   ranks    as   a  great 
philosopher,    and    also    made   some    extremely   important 
advances   in   pure  mathematics,   his  astronomical  writings 
were  of  little  value  and  in  many  respects  positively  harmful. 
In   his  Principles  of  Philosophy   (1644)   he   gave,   among 
some   wholly   erroneous   propositions,   a   fuller  and   more 

*  Also  frequently  referred  to  by  the  Latin  name  Cartesius. 


$$  162,  163]         The   Velocity  of  Light ;  Descartes  209 

general  statement  of  the  first  law  of  motion  discovered 
by  Galilei  (chapter  vi.,  §§  130,  133),  but  did  not  support  it 
by  any  evidence  of  value.  The  same  book  contained  an  i 
exposition  of  his  famous  theory  of  vortices,  which  was  an 
attempt  to  explain  the  motions  of  the  bodies  of  the  solar  ; 
system  by  means  of  a  certain  combination  of  vortices  or  i 
eddies.  The  theory  was  unsupported  by  any  experimental 
evidence,  and  it  was  not  formulated  accurately  enough  to 
be  capable  of  being  readily  tested  by  comparison  with 
actual  observation ;  and,  unlike  many  erroneous  theories 
(such  as  the  Greek  epicycles),  it  in  no  way  led  up  to 
or  suggested  the  truer  theories  which  followed  it.  But 
"  Cartesianism,"  both  in  philosophy  and  in  natural  science, 
became  extremely  popular,  especially  in  France,  and  its 
vogue  contributed  notably  to  the  overthrow  of  the  authority 
of  Aristotle,  already  shaken  by  thinkers  like  Galilei  and 
Bacon,  and  thus  rendered  men's  minds  a  little  more  ready 
to  receive  new  ideas  :  in  this  indirect  way,  as  well  as  by 
his  mathematical  discoveries,  Descartes  probably  con- 
tributed something  to  astronomical  progress. 


14 


CHAPTER   IX. 

UNIVERSAL    GRAVITATION. 

4  Nature  and  Nature's  laws  lay  hid  in  night ; 
God  said  'Let  Newton  be!'  and  all  was  light." 

POPE. 

164.  NEWTON'S  life  may  be  conveniently  divided  into  three 
portions.  First  came  22  years  (1643-1665)  of  boyhood 
and  undergraduate  life ;  then  followed  his  great  productive 
period,  of  almost  exactly  the  same  length,  culminating  in 
the  publication  of  the  Prindpia  in  1687  ;  while  the  rest  of 
his  life  (1687-1727),  which  lasted  nearly  as  long  as  the 
other  two  periods  put  together,  was  largely  occupied  with 
official  work  and  studies  of  a  non-scientific  character,  and 
was  marked  by  no  discoveries  ranking  with  those  made 
in  his  middle  period,  though  some  of  his  earlier  work 
received  important  developments  and  several  new  results 
of  decided  interest  were  obtained. 

165.  Isaac  Newton  was  born  at  Woolsthorpe,  near 
Grantham,  in  Lincolnshire,  on  January  4th,  1643;*  this 
was  very  nearly  a  year  after  the  death  of  Galilei,  and  a 
few  months  after  the  beginning  of  our  Civil  Wars.  His 
taste  for  study  does  not  appear  to  have  developed  very 
earlv  in  life,  but  ultimately  became  so  marked  that,  after 

*  According  to  the  unreformed  calendar  (O.S.)  then  in  use  in 
England,  the  date  was  Christmas  Day,  1642.  To  facilitate  comparison 
with  events  occurring  out  of  England,  I  have  used  throughout  this 
and  the  following  chapters  the  Gregorian  Calendar  (N.S.),  which  was 
at  this  time  adopted  in  a  large  part  of  the  Continent  (cf.  chapter  n., 

§22). 


CH.  ix.;  M  164—  i68j        NewtoiCs  Early  Life  211 

some  unsuccessful  attempts  to  turn  him  into  a  farmer,'he 
was  entered  at  Trinity  College,  Cambridge,  in  1661. 

Although  probably  at  first  rather  more  backward  than 
most  undergraduates,  he  made  extremely  rapid  progress 
in  mathematics  and  allied  subjects,  and  evidently  gave  his 
teachers  some  trouble  by  the  rapidity  with  which  he 
absorbed  what  little  they  knew.  He  met  with  Euclid's 
Elements  of  Geometry  for  the  first  time  while  an  under- 
graduate, but  is  reported  to  have  soon  abandoned  it  as 
being  "a  trifling  book,"  in  favour  of  more  advanced  reading. 
In  January  1665  he  graduated  in  the  ordinary  course  as 
Bachelor  of  Arts. 

1 66.  The   external   events  of  Newton's  life  during  the 
next  22  years  may  be  very   briefly  dismissed.      He   was 
elected  a  Fellow  in  1667,  became  M.A.  in  due  course  in 
the  following  year,  and  was  appointed  Lucasian  Professor 
of  Mathematics,  in  succession  to  his  friend  Isaac  Barrow, 
in  1669.     Three  years  later  he  was  elected  a  Fellow  of  the 
recently  founded  Royal  Society.     With  the  exception   of 
some  visits  to  his  Lincolnshire  home,  he  appears  to  have 
spent  almost  the  whole  period  in  quiet  study  at  Cambridge, 
and  the  hiit  »ry  of  his  life  is  almost  exclusively  the  history 
of  his  sucies  ive  discoveries. 

167.  His  scientific  work  falls    into    three   main  groups, 
astronomy  (including  dynamics),  optics,  and  pure  mathe- 
matics.   He  also  spent  a  good  deal  of  time  on  experimental 
work  in  chemistry,  as  well  as  on  heat  and  other  branches 
of  physics,  and  in  the  latter  half  of  his  life  devoted  much 
attention  to  questions  of  chronology  and  theology ;  in  none 
of  these  subjects,  however,  did  he  produce  results  of  much 
importance. 

1 68.  In  forming  an  estimate  of  Newton's  genius  it  is  of 
course  important  to  bear  in  mind  the  range  of  subjects 
with  which  he  dealt ;  from  our  present  point  of  view,  how- 
ever, his  mathematics  only  presents  itself  as  a  tool  to  be 
used  in  astronomical  work ;  and  only  those  of  his  optical 
discoveries  which  are  of  astronomical  importance  need  be 
mentioned   here.      In    1668   he   constructed  a   reflecting 
telescope,  that  is,  a  telescope  in  which  the  rays  of  light  from 
the  object  viewed  are  concentrated  by  means  of  a  curved 
mirror  instead  of  by  a  lens,  as  in  the  refracting  telescopes 


212  A  Short  History  of  Astronomy  [€H.  IX. 

of  Galilei  and  Kepler.  Telescopes  on  this  principle,  differ- 
ing however  in  some  important  particulars  from  Newton's, 
had  already  been  described  in  1663  by  James  Gregory 
(1638-1675),  with  whose  i  kas  Newton  was  acquainted,  but 
it  does  not  appear  that  Gregory  had  actually  made  an 
instrument.  Owing  to  mechanical  difficulties  in  construction, 
half  a  century  elapsed  before  reflecting  telescopes  were 
made  which  could  compete  with  the  best  refractors  of  the 
time,  and  no  important  astrcno  nical  discoveries  were  made 
with  them  before  the  time  of  William  Herschel  (chapter  xn.), 
more  than  a  century  after  the  original  invention. 

Newton's  discovery  of  the  effect  of  a  prism  in  resolving 
a  beam  of  white  light  into  different  colours  is  in  a  sense 
the  basis  of  the  method  of  spectrum  analysis  (chapter  xin., 
§  299),  to  which  so  many  astronomical  discoveries  of  the 
last  40  years  are  due. 

169.  The  ideas  by  which  Newton  is  best  known  in  each 
of  his  three  great  subjects — gravitation,  his  theory  of 
colours,  and  fluxions — seem  to  have  occurred  to  him 
and  to  have  been  partly  thought  out  within  less  than  two 
years  after  he  took  his  degree,  that  is  before  he  was  24. 
His  own  account — written  many  years  afterwards — gives 
a  vivid  picture  of  his  extraordinary  mental  activity  at  this 
time  : — 

"  In  the  beginning  of  the  year  1665  I  found  the  method  of 
approximating  Series  and  the  Rule  for  reducing  any  dignity  of 
any  Binomial  into  such  a  series.  The  same  year  in  May  I 
found  the  method  of  tangents  of  Gregory  and  Slusius,  and  in 
November  had  the  direct  method  of  Fluxions,  and  the  next 
year  in  January  had  the  Theory  of  Colours,  and  in  May  following 
I  had  entrance  into  the  inverse  method  of  Fluxions.  And  the 
same  year  I  began  to  think  of  gravity  extending  to  the  orb 
of  the  Moon,  and  having  found  out  how  to  estimate  the  force 
with  which  [a]  globe  revolving  within  a  sphere  presses  the 
surface  of  the  sphere,  from  Kepler's  Rule  of  the  periodical  times 
of  the  Planets  being  in  a  sesquialterate  proportion  of  their 
distances  from  the  centers  of  their  orbs  I  deduced  that  the 
forces  which  keep  the  Planets  in  their  orbs  must  [be]  reciprocally 
as  the  squares  of  their  distances  from  the  centers  about  which 
they  revolve  :  and  thereby  compared  the  force  requisite  to  keep 
the  Moon  in  her  orb  with  the  force  of  gravity  at  the  surface 
of  the  earth,  and  found  them  answer  pretty  nearly.  All  this 


§$169,170]  First  Discoveries :    Gravity  213 

was  in  the  two  plague  years  of  1665  and  1666,  for  in  those 
days  I  was  in  the  prime  of  my  age  for  invention,  arid  minded 
Mathematicks  and  Philosophy  more  than  at  any  time  since."  * 

170.  He  spent  a  considerable  part  of  this  time  (1665- 
1666)  at  Woolsthorpe,  on  account  of  the  prevalence  of 
the  plague. 

The  well-known  story,  that  he  was  set  meditating  on 
gravity  by  the  fall  of  an  apple  in  the  orchard,  is  based 
on  good  authority,  and  is  perfectly  credible  in-  the  sense 
that  the  apple  may  have  reminded  him  at  that  particular 
time  of  certain  problems  connected  with  gravity.  That 
the  apple  seriously  suggested  to  him  the  existence  of  the 
problems  or  any  key  to  their  solution  is  wildly  improbable. 

Several  astronomers  had  already  speculated  on  the 
"  cause  "  of  the  known  motions  of  the  planets  and  satellites  ; 
that  is  they  had  attempted  to  exhibit  these  motions  as 
consequences  of  some  more  fundamental  and  more  general 
laws.  Kepler,  as  we  have  seen  (chapter  vn.,  §  150),  had 
pointed  out  that  the  motions  in  question  should  not  be 
considered  as  due  to  the  influence  of  mere  geometrical 
points,  such  as  the  centres  of  the  old  epicycles,  but  to 
that  of  other  bodies  ;  and  in  particular  made  some  attempt 
to  explain  the  motion  of  the  planets  as  due  to  a  special 
kind  of  influence  emanating  from  the  sun.  He  went, 
however,  entirely  wrong  by  looking  for  a  force  to  keep 
up  the  motion  of  the  planets  and  as  it  were  push  them 
along.  Galilei's  discovery  that  the  motion  of  a  body 
goes  on  indefinitely  unless  there  is  some  cause  at  work 
to  alter  or  stop  it,  at  once  put  a  new  aspect  on  this  as 
on  other  mechanical  problems ;  but  he  himself  did  not 
develop  his  idea  in  this  particular  direction.  Giovanni 
Alfonso  Borelli  (1608-1679),  in  a  book  on  Jupiter's  satellites 
published  in  1666,  and  therefore  about  the  time  of  Newton's 
first  work  on  the  subject,  pointed  out  that  a  body  revolving 
in  a  circle  (or  similar  curve)  had  a  tendency  to  recede 
from  the  centre,  and  that  in  the  case  of  the  planets  this 
might  be  supposed  to  be  counteracted  by  some  kind  of 
attraction  towards  the  sun.  We  have  then  here  the  idea— 

*  From  a  MS.  among  the  Portsmouth  Papers,  quoted  in  the  Preface 
to  the  Catalogue  of  the  Portsmouth  Papers. 


214 


A  Short  History  of  Astronomy 


[CH.  IX. 


in  a  very  indistinct  form  certainly — that  the  motion  of  a 
planet  is  to  be  explained,  not  by  a  force  acting  in  the 
direction  in  which  it  is  moving,  but  by  a  force  directed 
towards  the  sun,  that  is  about  at  right  angles  to  the 
direction  of  the  planet's  motion.  Huygens  carried  this 
idea  much  further — though  without  special  reference  to 
astronomy — and  obtained  (chapter  vin.,  §  158)  a  numerical 
measure  for  the  tendency  of  a  body  moving  in  a  circle 
to  recede  from  the  centre,  a  tendency  which  had  in  some 
way  to  be  counteracted  if  the  body  was  not  to  fly  away. 
Huygens  published  his  work  in  1673,  some  years  after 
Newton  had  obtained  his  corresponding  result,  but  before 
he  had  published  anything ;  and  there  can  be  no  doubt 
that  the  two  men  worked  quite  independently. 

171.  Viewed   as  a   purely  general   question,  apart  from 
its  astronomical  applications,  the  problem  may  be  said  to 

be  to  examine  under 
what  conditions  a  body 
can  revolve  with  uniform 
speed  in  a  circle. 

Let  A  represent  the 
position  at  a  certain 
instant  of  a  body  which 
is  revolving  with  uniform 
speed  in  a  circle  of 
centre  o.  Then  at  this 
instant  the  body  is 
moving  in  the  direction 
of  the  tangent  A  a  to 
the  circle.  Conse- 
quently by  Galilei's  First 
Law  (chapter  vi., 
§§  130,  133);  if  left  to 
itself  and  uninfluenced  by  any  other  body,  it  would  con- 
tinue to  move  with  the  same  speed  and  in  the  same 
direction,  i.e.  along  the  line  A  a,  and  consequently  would 
be  found  after  some  time  at  such  a  point  as  a.  But 
actually  it  is  found  to  be  at  B  on  the  circle.  Hence  some 
influence  must  have  been  at  work  to  bring  it  to  B  instead 
of  to  a.  But  B  is  nearer  to  the  centre  of  the  circle  than 
a  is;  hence  some  influence  must  be  at  work  tending 


FIG.  70. — Motion  in  a  circle. 


$$  1 7 1.  172]  Motion  in  a   Circle  215 

constantly  to  draw  the  body  towards  o,  or  counteracting 
the  tendency  which  it  has,  in  virtue  of  the  First  Law  of 
Motion,  to  get  farther  and  farther  away  from  o.  To 
express  either  of  these  tendencies  numerically  we  want  a 
more  complex  idea  than  that  of  velocity  or  rate  of  motion, 
namely  acceleration  or  rate  of  change  of  velocity,  an  idea 
which  Galilei  added  to  science  in  his  discussion  of  the 
law  of  falling  bodies  (chapter  vi.,  §§  116,  133).  A  falling 
body,  for  example,  is  moving  after  one  second  with  the 
velocity  of  about  32  feet  per  second,  after  two  seconds 
with  the  velocity  of  64,  after  three  seconds  with  the  velocity 
of  96,  and  so  on ;  thus  in  every  second  it  gains  a  downward 
velocity  of  32  feet  per  second;  and  this  may  be  expressed 
otherwise  by  saying  that  the  body  has  a  downward  accele- 
ration of  32  feet  per  second  per  second.  A  further  in- 
vestigation of  the  motion  in  a  circle  shews  that  the  motion 
is  completely  explained  if  the  moving  body  has,  in  addition 
to  its  original  velocity,  an  acceleration  of  a  certain  magnitude 
directed  towards  the  centre  of  the  circle.  It  can  be  shewn 
further  that  the  acceleration  may  be  numerically  expressed 
by  taking  the  square  of  the  velocity  of  the  moving  body 
(expressed,  say,  in  feet  per  second),  and  dividing  this  by 
the  radius  of  the  circle  in  feet.  If,  for  example,  the  body 
is  moving  in  a  circle  having  a  radius  of  four  feet,  at  the 
rate  of  ten  feet  a  second,  thtn  the  acceleration  towards 

the  centre  is  (—         —  =  J  25  feet  per  second  per  second. 

These  results,  with  others  of  a  similar  character,  were 
first  published  by  Huygens — not  of  course  precisely  jn  this 
form — in  his  book  on  the  Pendulum  Clock  (chapter  vin., 
§  158) ;  and  discovered  independently  by  Newton  in  1666. 

If  then  a  body  is  seen  to  move  in  a  circle,  its  motion 
becomes  intelligible  if  some  other  body  can  be  discovered 
which  produces  this  acceleration.  In  a  common  case,  such 
as  when  a  stone  is  tied  to  a  string  and  whirled  round, 
this  acceleration  is  produced  by  the  string  which  pulls 
the  stone  ;  in  a  spinning-top  the  acceleration  of  the  outer 
parts  is  produced  by  the  forces  binding  them  on  to  the 
inner  part,  and  so  on. 

172.  In  the  most  important  cases  of  this  kind  which 
occur  in  astronomy,  a  planet  is  known  to  revolve  round 


216  A  Short  History  of  Astronomy  [CH.  ix. 

the  sun  in  a  path  which  does  not  differ  much  from  a 
circle.  If  we  assume  for  the  present  that  the  path  is 
actually  a  circle,  the  planet  must  have  an  acceleration  to- 
wards the  centre,  and  it  is  possible  to  attribute  this  to  the 
influence  of  the  central  body,  the  sun.  In  this  way  arises 
the  idea  of  attributing  to  the  sun  the  power  of  influencing 
in  some  way  a  planet  which  revolves  round  it,  so  as  to 
give  it  an  acceleration  towards  the  sun  ;  and  the  question 
at  once  arises  of  how  this  "  influence  "  differs  at  different 
distances.  To  answer  this  question  Newton  made  use  of 
Kepler's  Third  Law  (chapter  vii.,  §  144).  We  have  seen 
that,  according  to  this  law,  the  squares  of  the  times  of 
revolution  of  any  two  planets  are  proportional  to  the  cubes 
of  their  distances  from  the  sun  ;  but  the  velocity  of  the 
planet  may  be  found  by  dividing  the  length  of  the  path 
it  travels  in  its  revolution  round  the  sun  by  the  time  of 
the  revolution,  and  this  length  is  again  proportional  to  the 
distance  of  the  planet  from  the  sun.  Hence  the  velocities 
of  the  two  planets  are  proportional  to  their  distances  from 
the  sun,  divided  by  the  times  of  revolution,  and  conse- 
quently the  squares  of  the  velocities  are  proportional  to 
the  squares  of  the  distances  from  the  sun  divided  by  the 
squares  of  the  times  of  revolution.  Hence,  by  Kepler's 
law,  the  squares  of  the  velocities  are  proportional  to  the 
squares  of  the  distances  divided  by  the  cubes  of  the  dis- 
tances, that  is  the  squares  of  the  velocities  are  inversely 
proportional  to  the  distances,  the  more  distant  planet 
having  the  less  velocity  and  vice  versa.  Now  by  the 
formula  of  Huygens  the  acceleration  is  measured  by  the 
square  of  the  velocity  divided  by  the  radius  of  the  circle 
(which  in  this  case  is  the  distance  of  the  planet  from  the 
sun).  The  accelerations  of  the  two  planets  towards  the 
sun  are  therefore  inversely  proportional  to  the  distances 
each  multiplied  by  itself,  that  is  are  inversely  proportional 
to  the  squares  of  the  distances.  Newton's  first  result 
therefore  is :  that  the  motions  of  the  planets — regarded  as 
moving  in  circles,  and  in  strict  accordance  with  Kepler's 
Third  Law — can  be  explained  as  due  to  the  action  of  the 
sun,  if  the  sun  is  supposed  capable  of  producing  on  a 
planet  an  acceleration  towards  the  sun  itself  which  is 
proportional  to  the  inverse  square  of  its  distance  from 


§  i73l  The  Law  of  the  Inverse  Square  2 1 7 

the  sun ;  i.e.  at  twice  the  distance  it  is  |  as  great,  at  three 
times  the  distance  £  as  great,  at  ten  times  the  distance  T^ 
as  great,  and  so  on. 

The  argument  may  perhaps  be  made  clearer  by  a 
jnumericalexample.  In  round  numbers  Jupiter's  distance 
"from  tKe~sun  is  fitfe  times  as  great  as  that  of  the  earth, 
and  Jupiter  takes  12  years  to  perform  a  revolution  round 
the  sun,  whereas  the  earth  takes  one.  Hence  Jupiter  goes 
in  12  years  five  times  as  far  as  the  earth  goes  in  one,  and 
Jupiter's  velocity  is  therefore  about  T5^  that  of  the  earth's, 
or  the  two  velocities  are  in  the  ratio  of  5  to  12  ;  the 
squares  of  the  velocities  are  therefore  as  5X5toi2Xi2, 
or  as  25  to  144.  The  accelerations  of  Jupiter  and  of  the 
earth  towards  the  sun  are  therefore  as  25-^-5  to  144, 
or  as  5  to  144;  hence  Jupiter's  acceleration  towards  the 
sun  is  about  ^g-  that  of  the  earth,  and  if  we  had  taken 
more  accurate  figures  this  fraction  would  have  come  out 
more  nearly  ^V  Hence  at  five  times  the  distance  the 
acceleration  is  25  times  less. 

Thisjaw  of  the^ inverse  square,  as  it  may  be  called,  is 
also  the  law  according  to  which  the  light  emitted  from  the 
sun  or  any  other  bright  body  varies,  and  would  on  this 
account  also  be  not  unlikely  to  suggest  itself  in  connection 
with  any  kind  of  influence  emitted  from  the  sun. 

173.  The  next  step  in  Newton's  investigation  was  to  see 
whether  the  motion  of  the  moon  round  the  earth  could  be 
explained  in  some  similar  way.  By  the  same  argument  as 
before,  the  moon  could  be  shewn  to  have  an  acceleration 
towards  the  earth.  Now  a  stone  if  let  drop  falls  down- 
wards, that  is  in  the  direction  of  the  centre  of  the  earth, 
and,  as  Galilei  had  shewn  (chapter  vi.,  §  133),  this 
motion  is  one  of  uniform  acceleration';  if,  in  accordance 
with  the  opinion  generally  held  at  that  time,  the  motion 
is  regarded  as  being  due  to  the  earth,  we  may  say  that 
the  earth  has  the  power  of  giving  an  acceleration  towards 
its  own  centre  to  bodies  near  its  surface.  Newton  noticed 
that  this  power  extended  at  any  rate  to  the  tops  of  moun- 
tains, and  it  occurred  to  him  that  it  might  possibly  extend 
as  far  as  the  moon  and  so  give  rise  to  the  required 
acceleration.  Although,  however,  the  acceleration  of  falling 
bodies,  as  far  as  was  known  at  the  time,  was  the  same  for 


218  A  Short  History  of  Astronomy  [Cn.  ix. 

terrestrial  bodies  wherever  situated,  it  was  probable  that 
at  such  a  distance  as  that  of  the  moon  the  acceleration 
caused  by  the  earth  would  be  much  less.  Newton  assumed 
as  a  working  hypothesis  that  the  acceleration  diminished 
according  to  the  same  law  which  he  had  previously  arrived 
at  in  the  case  of  the  sun's  action  on  the  planets,  that  is 
that  the  acceleration  produced  by  the  earth  on  any  body 
is  inversely  proportional  to  the  square  of  the  distance  of 
the  body  from  the  centre  of  the  earth. 

It  may  be  noticed  that  a  difficulty  arises  here  which  did 
not  present  itself  in  the  corresponding  case  of  the  planets. 
The  distances  of  the  planets  from  the  sun  being  large 
compared  with  the  size  of  the  sun,  it  makes  little  difference 
whether  the  planetary  distances  are  measured  from  the 
centre  of  the  sun  or  from  any  other  point  in  it.  The  same 
is  true  of  the  moon  and  earth ;  but  when  we  are  comparing 
the  action  of  the  earth  on  the  moon  with  that  on  a  stone 
situated  on  or  near  the  ground,  it  is  clearly  of  the  utmost 
importance  to  decide  whether  the  distance  of  the  stone 
is  to  be  measured  from  the  nearest  point  of  the  earth, 
a  few  feet  off,  from  the  centre  of  the  earth,  4000  miles 
off,  or  from  some  other  point.  Provisionally  at  any  rate 
Newton  decided  on  measuring  from  the  centre  of  the 
earth. 

It  remained  to  verify  his  conjecture  in  the  case  of  the 
moon  by  a  numerical  calculation ;  this  could  easily  be  done 
if  certain  things  were  known,  viz.  the  acceleration  of  a 
falling  body  on  the  earth,  the  distance  of  the  surface  of 
the  earth  from  its  centre,  the  distance  of  the  moon,  and 
the  time  taken  by  the  moon  to  perform  a  revolution  round 
the  earth.  The  first  of  these  was  possibly  known  with  fair 
accuracy  ;  the  last  was  well  known ;  and  it  was  also  known 
that  the  moon's  distance  was  about  60  times  the  radius  of 
the  earth.  How  accurately  Newton  at  this  time  knew  the 
size  of  the  earth  is  uncertain.  Taking  moderately  accurate 
figures,  the  calculation  is  easily  performed.  In  a  month  of 
about  27  days  the  moon  moves  about  60  times  as  far  as 
the  distance  round  the  earth;  that  is  she  moves  about 
60  x  24,000  miles  in  27  days,  which  is  equivalent  to  about 
3,300  feet  per  second.  The  acceleration  of  the  moon  is 
therefore  measured  by  the  square  of  this,  divided  by  the 


§  173]  Extension  of  Gravity  to  the  Moon  2 1 9 

distance  of  the  moon  (which  is  60   times  the  radius  of  the 

earth,  or  20,000,000  feet) :  that  is,  it  is    -^^— 

60  x  2. -,000,000' 

which  reduces  to  about  y-J-^.  Consequently,  if  the  law  of 
the  inverse  square  holds,  the  acceleration  of  a  falling  body 
at  the  surface  of  the  earth,  which  is  60  times  nearer  to  the 

centre  than  the  moon  is,  should  be    — -.   or  between 

no 

32  and  33  ;  but  the  actual  acceleration  of  falling  bodies 
is  rather  more  than  32.  The  argument  is  therefore 
satisfactory,  and  Newton's  hypothesis  is  so  far  verified. 

The  analogy  thus  indicated  between  the  motion  of  the 
moon  round  the  earth  and  the  motion  of  a  falling  stone 
may  be  illustrated  by  a  comparison,  due  to  Newton,  of  the 
moon  to  a  bullet  shot  horizontally  out  of  a  gun  from  a 
high  place  on  the  earth.  Let  the  bullet  start  from  B  in 
fig.  71,  then  moving  at  first  horizontally  it  will  describe  a 
curved  path  and  reach  the  ground  at  a  point  such  as  c, 
at  some  distance  from  the  point  A,  vertically  underneath 
its  starting-point.  If  it  were  shot  out  with  a  greater  velocity, 
its  path  at  first  would  be  flatter  and  it  would  reach  the 
ground  at  a  point  c'  beyond  c  ;  if  the  velocity  were  greater 
still,  it  would  reach  the  ground  at  c"  or  at  c"' ;  and  it 
requires  only  a  slight  effort  of  the  imagination  to  conceive 
that,  with  a  still  greater  velocity  to  begin  with,  it  would  miss 
the  earth  altogether  and  describe  a  circuit  round  it,  such 
as  B  D  E.  This  is  exactly  what  the  moon  does,  the,  only 
difference  being  th^t  the  moon  is  at  a  much  greater  distance 
than  we  have  supposed  the  bullet  to  be,  and  that  her 
motion  has  not  been  produced  by  anything  analogous  to 
the  gun ;  but  the  motion  being  once  there  it  is  immaterial 
how  it  was  produced  or  whether  it  was  ever  produced  in 
the  past.  We  may  in  fact  say  of  the  moon  "  that  she  is  a 
falling  body,  only  she  is  going  so  fast  and  is  so  far  off  that 
she  falls  quite  round  to  the  other  side  of  the  earth,  instead 
of  hitting  it ;  and  so  goes  on  for  ever."  * 

In  the  memorandum  already  quoted  (§  169)  Newton 
speaks  of  the  hypothesis  as  fitting  the  facts  "  pretty 
nearly";  but  in  a  letter  of  earlier  date  (June  2oth,  1686) 

*  W.  K.  Clifford,  Aims  and  Instruments  of  Scientific  Thought. 


220 


A  Short  History  of  Astronomy 


[CH     IX. 


he  refers  to  the  calculation  as  not  having  been  made  accu- 
rately enough.  It  is  probable  that  he  used  a  seriously 
inaccurate  value  of  the  size  of  the  earth,  having  overlooked 
the  measurements  of  Snell  and  Norwood  (chapter  VIIL, 
§  159) ;  it  is  known  that  even  at  a  later  stage  he  was  unable 


FIG.  71. — The  moon  as  a  projectile. 


to  deal  satisfactorily  with  the  difficulty  above  mentioned, 
as  to  whether  the  earth  might  for  the  purposes  of  the 
problem  be  identified  with  its  centre ;  and  he  was  of  course 
aware  that  the  moon's  path  differed  considerably  from  a 
circle.  The  view,  said  to  have  been  derived  from  Newton's 
conversation  many  years  afterwards,  that  he  was  so  dis- 
satisfied with  his  results  as  to  regard  his  hypothesis  as 


$§  174,  ITS]    The  Motion  of  the  Moon,  and  of  the  Planets      221 

substantially  defective,  is  possible,  but  by  no  means  certain  ; 
whatever  the  cause  may  have  been,  he  laid  the  subject 
aside  for  some  years  without  publishing  anything  on  it,  and 
devoted  himself  chiefly  to  optics  and  mathematics. 

174.  Meanwhile  the  problem  of  the  planetary  motions 
was  one  of  the  numerous  subjects  of  discussion  among  the 
remarkable  group  of  men  who  were  the  leading  spirits  of 
the  .Royal  Society,  founded  in  1662.     Robert  Hooke  (1635- 
1703),  who  claimed  credit  for  most  of  the  scientific  dis- 
coveries of  the  time,  suggested  with  some  distinctness,  not 
later  than  1674,  that  the  motions  of  the  planets  might  be 
accounted  for  by  attraction  between  them  and  the  sun,  and 
referred  also  to  the  possibility  of  the  earth's  attraction  on 
bodies  varying  according  to  the  law  of  the  inverse  square. 
Christopher  Wren  (1632-1723),  better  known  as  an  architect 
than  as  a  man  of  science,  discussed  some  questions  of  this 
sort  with  Newton  in  1677,  and  appears  also  to  have  thought 
of  a  law  of  attraction  of  this  kind.    A  letter  of  H coke's  to 
Newton,  written  at  the  end  of  1679,  dealing  amongst  other 
things  with  the  curve  which  a  falling  body  would  describe, 
the  rotation  of  the  earth  being  taken  into  account,  stimulated 
Newton,  who  professed  that  at  this  time  his  "  affection  to 
philosophy  "  was  "  worn  out,"  to  go  on  with  his  study  of 
the  celestial  motions.     Picard's  more  accurate  measurement 
of  the  earth  (chapter  VIIL,  §  159)  was  now  well  known,  and 
Newton   repeated   his   former   calculation   of    the    moon's 
motion,  using  Picard's  improved  measurement,  and  found 
the  result  more  satisfactory  than  before. 

175.  At  the  same  time  (1679)  Newton  made  a  further 
discovery  of  the  utmost  importance  by  overcoming  some  of 
the  difficulties  connected  with  motion  in  a  path  other  than 
a  circle. 

He  shewed  that  if  a  body  moved  round  a  central  body, 
in  such  a  way  that  the  line  joining  the  two  bodies  sweeps 
out  equal  areas  in  equal  times,  as  in  Kepler's  Second  Law 
of  planetary  motion  (chapter  vii.,  §  141),  then  the  moving 
body  is  acted  on  by  an  attraction  directed  exactly  towards 
the  central  body ;  and  further  that  if  the  path  is  an  ellipse, 
with  the  central  body  in  one  focus,  as  in  Kepler's  First  Law 
of  planetary  motion,  then  this  attraction  must  vary  in 
different  parts  of  the  path  as  the  inverse  square  of  the 


222  A  Short  History  of  Astronomy  [CH.  IX. 

distance  between  the  two  bodies.  Kepler's  laws  of  planetary 
motion  were  in  fact  shewn  to  lead  necessarily  to  the 
conclusions  that  the  sun  exerts  on  a  planet  an  attraction 
inversely  proportional  to  the  square  of  the  distance  of  the 
planet  from  the  sun,  and  that  such  an  attraction  affords  a 
sufficient  explanation  of  the  motion  of  the  planet. 

Once   more,  however,   Newton   published   nothing   and 
"  threw  his  calculations  by,  being  upon  other  studies." 

176.  Nearly  five  years  later  the  matter  was  again  brought 
to  his  notice,  on  this  occasion  by  Edmund  Halley  (chap- 
ter x.,  §§  199-205),  whose  friendship  played  henceforward 
an    important   part  in   Newton's  life,  and  whose  unselfish 
devotion  to  the  great  astronomer  forms  a  pleasant  contrast 
to    the    quarrels    and    jealousies    prevalent  at    that  time 
between  so  many   scientific  men.      Halley,    not   knowing 
of  Newton's  work  in  1666,  rediscovered,  early  in  1684,  the 
law  of  the  inverse  square,  as  a  consequence   of  Kepler's 
Third  Law,  and  shortly  afterwards  discussed  with   Wren 
and   Hooke  what  was  the  curve  in  which  a  body  would 
move  if  acted   on   by  an  attraction  varying  according  to 
this  law ;  but  none  of  them  could  answer  the  question.* 
Later  in   the   year  Halley  visited  Newton  at   Cambridge 
and  learnt  from  him  the  answer.     Newton  had,  character- 
istically  enough,   lost    his    previous    calculation,    but  was 
able   to  work  it  out  again  and   sent   it   to  Halley  a  few 
months   afterwards.      This   time   fortunately  his   attention 
was  not  diverted  to  other  topics  ;  he  worked  out  at  once  a 
number  of  other  problems  of  motion,  and  devoted  his  usual 
autumn    course   of    University    lectures    to    the    subject. 
Perhaps  the  most  interesting  of  the  new  results  was  that 
Kepler's  Third  Law,  from  which    the  law  of  the   inverse 
square  had  been  deduced  in   1666,  only  on  the  supposition 
that  the  planets  moved  in  circles,  was  equally  consistent 
with   Newton's  law  when  the  paths  of  the  planets  were 
taken  to  be  ellipses. 

177.  At   the   end    of   the    year    1684    Halley   went   to 
Cambridge  again  and  urged  Newton  to  publish  his  results. 
In  accordance  with  this  request  Newton  wrote  out,  and  sent 

*  It  is  interesting  to  read  that  Wren  offered  a  prize  of  405.  to 
whichever  of  the  other  two  should  solve  this  the  central  problem  of 
the  solar  system. 


$$176—179]  Elliptic  Motion:  the  Principia  223 

to  the  Royal  Society,  a  tract  called  Propositioned  de  Motu> 
the  ii  propositions  of  which  contained  the  results  already 
mentioned  and  some  others  relating  to  the  motion  of 
bodies  under  attraction  to  a  centre.  Although  the  pro- 
positions were  given  in  an  abstract  form,  it  was  pointed  out 
that  certain  of  them  applied  to  the  case  of  the  planets. 
Further  pressure  from  Halley  persuaded  Newton  to  give 
his  results  a  more  permanent  form  by  embodying  them  in 
a  larger  book.  As  might  have  been  expected,  the  subject 
grew  under  his  hands,  and  the  great  treatise  which  resulted 
contained  an  immense  quantity  of  material  not  contained 
in  the  De  Motu.  By  the  middle  of  1686  the  rough  draft 
was  finished,  and  some  of  it  was  ready  for  press.  Halley 
not  only  undertook  to  pay  the  expenses,  but  superintended 
the  printing  and  helped  Newton  to  collect  the  astronomical 
data  which  were  necessary.  After  some  delay  in  the  press, 
the  book  finally  appeared  early  in  July  1687,  under  the 
title  Philosophiae  Naturalis  Principia  Mathematica. 

178.  The  Principia^  as  it  is  commonly  called,  consists  of 
three  books  in  addition  to  introductory  matter :  the  first 
book  dc  ils  generally  with  problems  of  the  motion  of  bodies, 
solved  for  the  most  part  in  an  abstract  form  without  special 
reference  to  astronomy  ;  the  second  book  deals  with  the 
motion  of  bodies  through  media  which  resist  their  motion, 
such   as    ordinary   fluids,    arid   is    of    comparatively   small 
astronomical  importance,   except  that   in  it   some   glaring 
inconsistencies   in    the   Cartesian    theory   of   vortices   are 
pointed  out ;  the  third  book  applies  to  the  circumstances 
of  the  actual  solar  system  the  results  already  obtained,  and 
is  in  fact  an  explanation  of  the  motions  of  the  celestial 
bodies  on  Newton's  mechanical  principles. 

179.  The  introductory  portion,  consisting  of  "  Definitions  " 
and  "Axioms,  or  Laws  of  Motion,"  forms  a  very  notable 
contribution  to  dynamics,  being  in  fact  the  first  coherent 
statement  of  the  fundamental  laws  according  to  which  the 
motions   of  bodies   are   produced   or   changed.      Newton 
himself  does   not   appear   to   have   regarded   this  part  of 
his    book    as    of    very   great   importance,    and  the    chief 
results  embodied  in  it,  being  overshadowed  as  it  were  by 
the  more  striking  discoveries   in  other  parts  of  the  book, 
attracted  comparatively  little  attention.    Much  of  it  must  be 


224  A  Short  History  of  Astronomy  [CH.  ix. 

passed  over  here,  but  certain  results  of  special  astronomical 
importance  require  to  be  mentioned. 

Galilei,  as  we  have  seen  (chapter  vi.,  §§  130,  133), 
was  the  first  to  enunciate  the  law  that  a  body  when  once 
in  motion  continues  to  move  in  the  same  direction  and 
at  the  same  speed  unless  some  cause  is  at  work  to  make 
it  change  its  motion.  This  law  is  given  by  Newton  in 
the  form  already  quoted  in  §  130,  as  the  first  of  three 
fundamental  laws,  and  is  now  commonly  known  as  the 
First  Law  of  Motion. 

Galilei  also  discovered  that  a  falling  body  moves  with 
continually  changing  velocity,  but  with  a  uniform  accelera- 
tion (chapter  vi.,  §  133),  and  that  this  acceleration  is  the 
same  for  all  bodies  (chapter  vi.,  §  116).  The  tendency  of 
a  body  to  fall  having  been  generally  recognised  as  due 
to  the  earth,  Galilei's  discovery  involved  the  recognition 
that  one  effect  of  one  body  on  another  may  be  an  accelera- 
tion produced  in  its  motion.  Newton  extended  this  idea 
by  shewing  that  the  earth  produced  an  acceleration  in  the 
motion  of  the  moon,  and  the  sun  in  the  motion  of  the 
planets,  and  was  led  to  the  general  idea  of  acceleration  in 
a  body's  motion,  which  might  be  due  in  a  variety  of  ways 
to  the  action  of  other  bodies,  and  which  could  conveniently 
be  taken  as  a  measure  of  the  effect  produced  by  one  body 
on  another. 

1 80.  To  these  ideas  Newton  added  the  very  important 
and  difficult  conception  of  mass. 

If  we  are  comparing  two  different  bodies  of  the  same 
material  but  of  different  sizes,  we  are  accustomed  to  think 
of  the  larger  one  as  heavier  than  the  other.  In  the  same 
way  we  readily  think  of  a  ball  of  lead  as  being  heavier 
than  a  ball  of  wood  of  the  same  size.  The  most  prominent 
idea  connected  with  "heaviness"  and  "lightness"  is  that 
of  the  muscular  effort  required  to  support  or  to  lift  the 
body  in  question ;  a  greater  effort,  for  example,  is  required 
to  hold  the  leaden  ball  than  the  wooden  one.  Again,  the 
leaden  ball  if  supported  by  an  elastic  string  stretches  it 
farther  than  does  the  wooden  ball ;  or  again,  if  they  are 
placed  m  the  scales  of  a  balance,  the  lead  sinks  and  the 
wood  rises.  All  these  effects  we  attribute  to  the  "  weight " 
of  the  two  bodies,  and  the  weight  we  are  mostly  accustomed 


§  i8o]  Newton's  Laws  of  Motion :  Mass  225 

to  attribute  in  some  way  to  the  action  of  the  earth  on 
the  bodies.  The  ordinary  process  of  weighing  a  body  in 
a  balance  shews,  further,  that  we  are  accustomed  to  think 
of  weight  as  a  measurable  quantity.  On  the  other  hand, 
we  know  from  Galilei's  result,  which  Newton  tested  very 
carefully  by  a  series  of  pendulum  experiments,  that  the 
leaden  and  the  wooden  ball,  if  allowed  to  drop,  fall  with 
the  same  acceleration.  If  therefore  we  measure  the  effect 
which  the  earth  produces  on  the  two  balls  by  their 
acceleration,  then  the  earth  affects  them  equally ;  but  if 
we  measure  it  by  the  power  which  they  have  of  stretching 
strings,  or  by  the  power  which  one  has  of  supporting  the 
other  in  a  balance,  then  the  effect  which  the  earth  produces 
on  the  leaden  ball  is  greater  than  that  produced  on  the 
wooden  ball.  Taken  in  this  way,  the  action  of  the  earth 
on  either  ball  may  be  spoken  of  as  weight,  and  the  weight 
of  a  body  can  be  measured  by  comparing  it  in  a  balance 
with  standard  bodies. 

The  difference  between  two  such  bodies  as  the  leaden 
and  wooden  ball  may,  however,  be  recognised  in  quite 
a  different  way.  We  can  easily  see,  for  example,  that  a 
greater  effort  is  needed  to  set  the  one  in  motion  than 
the  other;  or  that  if  each  is  tied  to  the  end  of  a  string 
of  given  kind  and  whirled  round  at  a  given  rate,  the 
one  string  is  more  tightly  stretched  than  the  other.  In 
these  cases  the  attraction  of  the  earth  is  of  no  importance, 
and  we  recognise  a  distinction  between  the  two  bodies 
which  is  independent  of  the  attraction  of  the  earth.  This 
distinction  Newton  regarded  as  due  to  a  difference  in 
the  quantity  of  matter  or  material  in  the  two  bodies, 
and  to  this  quantity  he  gave  the  name  of  mass.  It  may 
fairly  be  doubted  whether  anything  is  gained  by  this  par- 
ticular definition  of  mass,  but  the  really  important  step 
was  the  distinct  recognition  of  mass  as  a  property  of  bodies, 
of  fundamental  importance  in  dynamical  questions,  and 
capable  of  measurement. 

Newton,  developing  Galilei's  idea,  gave  as  one  measure- 
ment of  the  action  exerted  by  one  body  on  another  the  pro- 
duct of  the  mass  by  the  acceleration  produced — a  quantity 
for  which  he  used  different  names,  now  replaced  by 
force.  The  weight  of  a  body  was  thus  identified  with  the 


226  A  Short  History  of  Astronomy  [CH.  ix. 

force  exerted  on  it  by  the  earth.  Since  the  earth  produces 
the  same  acceleration  in  all  bodies  at  the  same  place, 
it  follows  that  the  masses  of  bodies  at  the  same  place  are 
proportional  to  their  weights ;  thus  if  two  bodies  are  com- 
pared at  the  same  place,  and  the  weight  of  one  (as  shewn, 
for  example,  by  a  pair  of  scales)  is  found  to  be  ten  times 
that  of  the  other,  then  its  mass  is  also  ten  times  as 
great.  But  such  experiments  as  those  of  Richer  at  Cayenne 
(chapter  VIIL,  §  161)  shewed  that  the  acceleration  of  falling 
bodies  was  less  at  the  equator  than  in  higher  latitudes  ; 
so  that  if  a  body  is  carried  from  London  or  Paris  to 
Cayenne,  its  weight  is  altered  but  its  mass  remains  the 
same  as  before.  Newton's  conception  of  the  earth's 
gravitation  as  extending  as  far  as  the  moon  gave  further 
importance  to  the  distinction  between  mass  and  weight ; 
for  if  a  body  were  removed  from  the  earth  to  the  moon, 
then  its  mass  would  be  unchanged,  but  the  acceleration 
due  to  the  earth's  attraction  would  be  60  x  60  times  less, 
and  its  weight  diminished  in  the  same  proportion. 

Rules  are  also  given  for  the  effect  produced  on  a 
body's  motion  by  the  simultaneous  action  of  two  or  more 
forces.* 

A  further  principle  of  great  importance,  of  which  only 
very  indistinct  traces  are  to  be  found  before  Newton's 
time,  was  given  by  him  as  the  Third  Law  of  Motion  in 
the  form :  "  To  every  action  there  is  always  an  equal 
and  contrary  reaction ;  or,  the  mutual  actions  of  any  two 
bodies  are  always  equal  and  oppositely  directed."  Here 
action  and  reaction  are  to  be  interpreted  primarily  in  the 
sense  of  force:  If  a  stone  rests  on  the  hand,  the  force  with 
which  the  stone  presses  the  hand  downwards  is  equal  to 
that  with  which  the  hand  presses  the  stone  upwards  ;  if 
the  earth  attracts  a  stone  downwards  with  a  certain  force, 
then  the  stone  attracts  the  earth  upwards  with  the  same 
force,  and  so  on.  It  is  to  be  carefully  noted  that  if,  as 
in  the  last  example,  two  bodies  are  acting  on  one  another, 
the  accelerations  produced  are  not  the  same,  but  since  force 

*  The  familiar  parallelogram  of  forces,  of  which  earlier  writers  had 
had  indistinct  ideas,  was  clearly  stated  and  proved  in  the  intro- 
duction to  the  Prinapia,  and  was,  by  a  curious  coincidence,  published 
also  in  the  same  year  by  Varignon  and  Lami. 


$  i8i]  Mass:  Action  and  Reaction  227 

is  measured  by  the  product  of  mass  and  acceleration,  the 
body  with  the  larger  mass  receives  the  lesser  acceleration. 
In  the  case  of  a  stone  and  the  earth,  the  mass  of  the 
latter  being  enormously  greater,*  its  acceleration  is  enor- 
mously less  than  that  of  the  stone,  and  is  therefore  (in 
accordance  with  our  experience)  quite  insensible. 

181.  When  Newton  began  to  write  the  Principia  he  had 
probably  satisfied  himself  (§  173)  that  the  attracting  power 
of  the  earth  extended  as  far  as  the  moon,  and  that  the 
acceleration  thereby  produced  in  any  body — whether  the 
moon,  or  whether  a  body  close  to  the  earth — is  inversely 
proportional  to  the  square  of  the  distance  from  the  centre 
of  the  earth.  With  the  ideas  of  force  and  mass  this  result 
may  be  stated  in  the  form  :  the  earth  attracts  any  body  with 
a  force  inversely  proportional  to  the  square  of  the  distance 
from  the  earths  centre,  and  also  proportional  to  the  mass  of 
the  body, 

In  the  same  way  Newton  had  established  that  the 
motions  of  the  planets  could  be  explained  by  an  attraction 
towards  the  sun  producing  an  acceleration  inversely  pro- 
portional to  the  square  of  the  distance  from  the  sun's 
centre,  not  only  in  the  same  planet  in  different  parts  of  its 
path,  but  also  in  different  planets.  Again,  it  follows  from 
this  that  the  sun  attracts  any  planet  with  a  force  inversely 
proportional  to  the  square  of  the  distance  of  the  planet 
from  the  sun's  centre,  and  also  proportional  to  the  mass 
of  the  planet. 

But  by  the  Third  Law  of  Motion  a  body  experiencing  an 
attraction  towards  the  earth  must  in  turn  exert  an  equal 
attraction  on  the  earth ;  similarly  a  body  experiencing  an 
attraction  towards  the  sun  must  exert  an  equal  attraction 
on  the  sun.  If,  for  example,  the  mass  of  Venus  is  seven 
times  that  of  Mars,  then  the  force  with  which  the  sun 
attracts  Venus  is  seven  times  as  great  as  that  with  which 
it  would  attract  Mars  if  placed  at  the  same  distance  ;  and 
therefore  also  the  force  with  which  Venus  attracts  the 
sun  is  seven  times  as  great  as  that  with  which  Mars  would 
attract  the  sun  if  at  an  equal  distance  from  it.  Hence,  in 
all  the  cases  of  attraction  hitherto  considered  and  in 

*  It  is  between  13  and  14  billion  billion  pounds.  Sec  chapter  x. 
§219. 


228  A  Short  History  of  Astronomy  [CH.  IX. 

which  the  comparison  is  possible,  the  force  is  proportional 
not  only  to  the  mass  of  the  attracted  body,  but  also  to 
that  of  the  attracting  body,  as  well  as  being  inversely  pro- 
portional to  the  square  of  the  distance.  Gravitation  thus 
appears  no  longer  as  a  property  peculiar  to  the  central 
body  of  a  revolving  system,  but  as  belonging  to  a  planet 
in  just  the  same  way  as  to  the  sun,  and  to  the  moon  or 
to  a  stone  in  just  the  same  way  as  to  the  earth. 

Moreover,  the  fact  that  separate  bodies  on  the  surface 
of  the  earth  are  attracted  by  the  earth,  and  therefore  in 
turn  attract  it,  suggests  that  this  power  of  attracting  other 
bodies  which  the  celestial  bodies  are  shewn  to  possess 
does  not  belong  to  each  celestial  body  as  a  whole,  but  to 
the  separate  particles  making  it  up,  so  that,  for  example, 
the  force  with  which  Jupiter  and  the  sun  mutually  attract 
one  another  is  the  result  of  compounding  the  forces  with 
which  the  separate  particles  making  up  Jupiter  attract 
the  separate  particles  making  up  the  sun.  Thus  is 
suggested  finally  the  law  of  gravitation  in  its  most  general 
form :  every  particle  of  matter  attracts  every  other  particle 
with  ft  force  proportional  to  the  mass  of  each,  and  inversely 
proportional  to  the  square  of  the  distance  between  them* 

182.  In  all  the  astronomical  cases  already  referred  to 
the  attractions  between  the  various  celestial  bodies  have 
been  treated  as  if  they  were  accurately  directed  towards 
their  centres,  and  the  distance  between  the  bodies  has 
been  taken  to  be  the  distance  between  their  centres. 
Newton's  doubts  on  this  point,  in  the  case  of  the  earth's 
attraction  of  bodies,  have  been  already  referred  to  (§  173) ; 
but  early  in  1685  he  succeeded  in  justifying  this  assumption. 
By  a  singularly  beautiful  and  simple  course  of  reasoning 
he  shewed  (Principia^  Book  I.,  propositions  70,  71)  that,  if 
a  body  is  spherical  in  form  and  equally  dense  throughout, 
it  attracts  any  particle  external  to  it  exactly  as  if  its  whole 
mass  were  concentrated  at  its  centre.  He  shewed,  further, 
that  the  same  is  true  for  a  sphere  of  variable  density, 
provided  it  can  be  regarded  as  made  up  of  a  series  of 
spherical  shells,  having  a  common  centre,  each  of  uniform 

*  As  far  as  I  know  Newton  gives  no  short  statement  of  the  law 
in  a  perfectly  complete  and  general  form  ;  separate  parts  of  it  are 
given  in  different  passages  of  the  Principia. 


$$  i82,  183]  Universal  Gravitation  229 

density  throughout,  different  shells  being,  however,  of 
different  densities.  For  example,  the  result  is  true  for  a 
hollow  indiarubber  ball  as  well  as  for  a  solid  one,  but 
is  not  true  for  a  sphere  made  up  of  a  hemisphere  of  wood 
and  a  hemisphere  of  iron  fastened  together. 

183.  The  law  of  gravitation  being  thus  provisionally 
established,  the  great  task  which  lay  before  Newton,  and 
to  which  he  devotes  the  greater  part  of  the  first  and  third 
books  of  the  Principia^  was  that  of  deducing  from  it  and 
the  "  laws  of  motion  "  the  motions  of  the  various  members 
of  the  solar  system,  and  of  shewing,  if  possible,  that  the 
motions  so  calculated  agreed  with  those  observed.  If  this 
were  successfully  done,  it  would  afford  a  verification  of  the 
most  delicate  and  rigorous  character  of  Newton's  principles. 

The  conception  of  the  solar  system  as  a  mechanism,  each 
member  of  which  influences  the  motion  of  every  other 
member  in  accordance  with  one  universal  law  of  attraction, 
although  extremely  simple  in  itself,  is  easily  seen  to  give  rise 
to  very  serious  difficulties  when  it  is  proposed  actually  to 
calculate  the  various  motions.  If  in  dealing  with  the 
motion  of  a  planet  such  as  Mars  it  were  possible  to  regard 
Mars  as  acted  on  only  by  the  attraction  of  the  sun,  and  to 
ignore  the  effects  of  the  other  planets,  then  the  problem 
would  be  completely  solved  by  the  propositions  which 
Newton  established  in  1679  (§  I75)>  and  by  their  means  the 
position  of  Mars  at  any  time  could  be  calculated  with  any 
required  degree  of  accuracy.  But  in  the  case  which 
actually  exists  the  motion  of  Mars  is  affected  by  the  forces 
with  which  all  the  other  planets  (as  well  as  the  satellites) 
attract  it,  and  these  forces  in  turn  depend  on  the  position  of 
Mars  (as  well  as  upon  that  of  the  other  planets)  and  hence 
upon  the  motion  of  Mars.  A  problem  of  this  kind  in  all 
its  generality  is  quite  beyond  the  powers  of  any  existing 
mathematical  methods.  Fortunately,  however,  the  mass 
of  even  the  largest  of  the  planets  is  so  very  much  less  than 
that  of  the  sun,  that  the  motion  of  any  one  planet  is  only 
slightly  affected  by  the  others ;  and  it  may  be  regarded  as 
moving  very  nearly  as  it  would  move  if  the  other  planets 
did  not  exist,  the  effect  of  these  being  afterwards  allowed 
for  as  producing  disturbances  or  perturbations  in  its  path. 
Although  even  in  this  simplified  form  the  problem  of  the 


•f 

230  A  Short  History  of  Astronomy  [CH.  ix. 

motion  of  the  planets  is  one  of  extreme  difficulty  (cf. 
chapter  XL,  §  228),  and  Newton  was  unable  to  solve  it  with 
anything  like  completeness,  yet  he  was  able  to  point  out 
certain  general  effects  which  must  result  from  the  mutual 
action  of  the  planets,  the  most  interesting  being  the  slow 
forward  motion  of  the  apses  of  the  earth's  orbit,  which  had 
long  ago  been  noticed  by  observing  astronomers  (chapter  in., 
§  59).  Newton  also  pointed  out  that  Jupiter,  on  account 
of  its  great  mass,  must  produce  a  considerable  perturbation 
in  the  motion  of  its  neighbour  Saturn,  and  thus  gave  some 
explanation  of  an  irregularity  first  noted  by  Horrocks 
(chapter  VHI.,  §  156). 

184.  The  motion  of  the  moon  presents  special  difficulties, 
but  Newton,  who  was  evidently  much  interested  in  the 
problems  of  lunar  theory,  succeeded  in  overcoming  them 
much  more  completely  than  the  corresponding  ones 
connected  with  the  planets. 

The  moon's  motion  round  the  earth  is  primarily  due  to 
the  attraction  of  the  earth ;  the  perturbations  due  to  the 
other  planets  are  insignificant ;  but  the  sun,  which  though 
at  a  very  great  distance  has  an  enormously  greater  mass 
than  the  earth,  produces  a  very  sensible  disturbing  effect 
on  the  moon's  motion.  Certain  irregularities,  as  we  have 
seen  (chapter  H.,  §§  40,  48 ;  chapter  v.,  §  in),  had  already 
been  discovered  by  observation.  Newton  was  able  to 
shew  that  the  disturbing  action  of  the  sun  would  neces- 
sarily produce  perturbations  of  the  same  general  character 
as  those  thus  recognised,  and  in  the  case  of  the  motion  of 
the  moon's  nodes  and  of  her  apogee  he  was  able  to  get  a 
very  fairly  accurate  numerical  result;*  and  he  also  dis- 
covered a  number  of  other  irregularities,  for  the  most  part 
very  small,  which  had  not  hitherto  been  noticed.  He 
indicated  also  the  existence  of  certain  irregularities  in  the 
motions  of  Jupiter's  and  Saturn's  moons  analogous  to  those 
which  occur  in  the  case  of  our  moon. 

*  It  is  commonly  stated  that  Newton's  value  of  the  motion  of  the 
moon's  apses  was  only  about  half  the  true  value.  In  a  scholium 
of  the  Principia  to  prop.  35  of  the  third  book,  given  in  the  first 
edition  but  afterwards  omitted,  he  estimated  the  annual  motion  at 
40°,  the  observed  value  being  about  41°.  In  one  of  his  unpublished 
papers,  contained  in  the  Portsmouth  collection,  he  arrived  at  39°  by 
a  process  which  he  evidently  regarded  as  not  altogether  satisfactory. 


§$  184-186]  Universal  Gravitation  231 

185.  One  group  of  results  of  an  entirely  novel  character 
resulted  from  Newton's  theory  of  gravitation.     It  became 
for  the  first  time  possible  to  estimate  the  masses  of  some 
of  the  celestial  bodies,  by  comparing  the  attractions  exerted 
by  them  on  other  bodies  with  that  exerted  by  the  earth. 

The  case  of  Jupiter  may  be  given  as  an  illustration.  The 
time  of  revolution  of  Jupiter's  outermost  satellite  is  known 
to  be  about  16  days  16  hours,  and  its  distance  from 
Jupiter  was  estimated  by  Newton  (not  very  correctly)  at 
about  four  times  the  distance  of  the  moon  from  the  earth. 
A  calculation  exactly  like  that  of  §  172  or  §  173  shews  that 
the  acceleration  of  the  satellite  due  to  Jupiter's  attraction 
is  about  ten  times  as  great  as  the  acceleration  of  the  moon 
towards  the  earth,  and  that  therefore,  the  distance  being 
four  times  as  great,  Jupiter  attracts  a  body  with  a  force 
10  x  4  x  4  times  as  great  as  that  with  which  the  earth 
^attracts  a  body  at  the  same  distance  ;  consequently  Jupiter's 
"mass  is  160  times  that  of  the  earth.  This  process  of 
reasoning  applies  also  to  Saturn,  and  in  a  very  similar  way 
a  comparison  of  the  motion  of  a  planet,  Venus  for  example, 
round  the  sun  with  the  motion  of  the  moon  round  the 
earth  gives  a  relation  between  the  masses  of  the  sun  and 
earth.  In  this  way  Newton  found  the  mass  of  the  sun  to 
be  1067,  3021,  and  169282  times  greater  than  that  of 
Jupiter,  Saturn,  and  the  earth,  respectively.  The  corre- 
sponding figures  now  accepted  are  not  far  from  1047,  3530, 
324439.  The  large  error  in  the  last  number  is  due  to  the 
use  of  an  erroneous  value  of  the  distance  of  the  sun — then 
not  at  all  accurately  known — upon  which  depend  the  other 
distances  in  the  solar  system,  except  those  connected  with 
the  earth-moon  system.  As  it  was  necessary  for  the  em- 
ployment of  this  method  to  be  able  to  observe  the  motion 
of  some  other  body  attracted  by  the  planet  in  question,  it 
could  not  be  applied  to  the  other  three  planets  (Mars, 
Venus,  and  Mercury),  of  which  no  satellites  were  known. 

1 86.  From  the  equality  of  action  and  reaction  it  follows 
that,  since  the  sun  attracts  the  planets,  they  also  attract  the 
sun,  and  the  sun  consequently  is  in  motion,  though — owing 
to  the  comparative  smallness  of  the  planets — only  to  a  very 
small  extent.     It  follows  that  Kepler's  Third  Law  is  not 
strictly  accurate,  deviations  from  it  becoming  sensible   in 


232  A  Short  History  of  Astronomy  [Cn.  ix. 

the  case  of  the  large  planets  Jupiter  and  Saturn  (cf.  chap- 
ter vii.,  §  144).  It  was,  however,  proved  by  Newton  that 
in  any  system  of  bodies,  such  as  the  solar  system,  moving 
about  in  any  way  under  the  influence  of  their  mutual 
attractions,  there  is  a  particular  point,  called  the  centre  of 
gravity,  which  can  always  be  treated  as  at  rest ;  the  sun 
moves  relatively  to  this  point,  but  so  little  that  the  distance 
between  the  centre  of  the  sun  and  the  centre  of  gravity  can 
never  be  much  more  than  the  diameter  of  the  sun. 

It  is  perhaps  rather  curious  that  this  result  was  not  seized 
upon  by  some  of  the  supporters  of  the  Church  in  the  con- 
demnation of  Galilei,  now  rather  more  than  half  a  century 
old ;  for  if  it  was  far  from  supporting  the  view  that  the 
earth  is  at  the  centre  of  the  world,  it  at  any  rate  negatived 
that  part  of  the  doctrine  of  Coppernicus  and  Galilei  which 
asserted  the  sun  to  be  at  rest  in  the  centre  of  the  world. 
Probably  no  one  who  was  capable  of  understanding 
Newton's  book  was  a  serious  supporter  of  any  anti- 
Coppernican  system,  though  some  still  professed  them- 
selves obedient  to  the  papal  decrees  on  the  subject.* 

*  Throughout  the  Coppernican  controversy  up  to  Newton's  time 
it  had  been  generally  assumed,  both  by  Coppernicans  and  by  their 
opponents,  that  there  was  some  meaning  in  speaking  of  a  body  simply 
as  being  "at  rest"  or  "in  motion,"  without  any  reference  to  any 
other  body.  But  all  that  we  can  really  observe  is  the  motion  of  one 
body  relative  to  one  or  more  others.  Astronomical  observation  tells 
us,  for  example,  of  a  certain  motion  relative  to  one  another  of  the 
earth  and  sun  ;  and  this  motion  was  expressed  in  two  quite  different 
ways  by  Ptolemy  and  by  Coppernicus.  From  a  modern  standpoint 
the  question  ultimately  involved  was  whether  the  motions  of  the 
various  bodies  of  the  solar  system  relatively  to  the  earth  or  relatively 
to  the  sun  were  the  simpler  to  express.  If  it  is  found  convenient  to 
express  them — as  Coppernicus  and  Galilei  did — in  relation  to  the 
sun,  some  simplicity  of  statement  is  gained  by  speaking  of  the  sun 
as  "  fixed  "  and  omitting  the  qualification  "  relative  to  the  sun  "  in 
speaking  of  any  other  body.  The  same  motions  might  have  been 
expressed  relatively  to  any  other  body  chosen  at  will :  e.g.  to  one  of 
the  hands  of  a  watch  carried  by  a  man  walking  up  and  down  on  the 
deck  of  a  ship  on  a  rough  sea ;  in  this  case  it  is  clear  that  the  motions 
of  the  other  bodies  of  the  solar  system  relative  to  this  body  would  be 
excessively  complicated  ;  and  it  would  therefore  be  highly  inconvenient 
though  still  possible  to  treat  this  particular  body  as  "fixed." 

A  new  aspect  of  the  problem  presents  itself,  however,  when  an 
attempt — like  Newton's — is  made  to  explain  the  motions  of  bodies  of 
the  solar  system  as  the  result  of  forces  exerted  on  one  another  by 


$  187]         Relative  Motion:  the  Snap    jf  the  Earth         233 

187.  The  variation  of  the  ti«^  of  oscillation  of  a 
pendulum  in  different  parts  c"  -ne  earth,  discovered  by 
Richer  in  1672  (chapter  vin  <?i6r),  indicated  that  the 
earth  was  probably  not  a  sj  ^ere.  Newton  pointed  out 
that  this  departure  from  the  spherical  form  was  a  conse- 
quence of  the  mutual  gravitation  of  the  particles  making 
up  the  earth  and  of  the  earth's  rotation.  He  supposed  a 
canal  of  water  to  pass  from  the  pole  to  the  centre  of  the 
earth,  and  then  from  the  centre  to  a  point  on  the  equator 
(BO« A  in  fig.  72),  and  then  found  the  condition  that  these 
two  columns  of  water  OB,  o  A,  each  being  attracted  towards 
the  centre  of  the  earth,  should  balance.  This  method 
involved  certain  assumptions  as  to  the  inside  of  the  earth, 
of  which  little  can  be  said  to  be  known  even  now,  and 
consequently,  though  Newton's  general  result,  that  the 
earth  is  flattened  at  the  poles  and  bulges  out  at  the  equator, 
was  right,  the  actual  numerical  expression  which  he  found 
was  not  very  accurate.  If,  in  the  figure,  the  dotted  line  is 
a  circle  the  radius  of  which  is  equal  to  the  distance  of  the 

those  bodies.  If,  for  example,  we  look  at  Newton's  First  Law  of 
Motion  (chapter  vi.,  §  130),  we  see  that  it  has  no  meaning,  unless  we 
know  what  are  the  body  or  bodies  relative  to  which  the  motion  is 
being  expressed ;  a  body  at  rest  relatively  to  the  earth  is  moving 
relatively  to  the  sun  or  to  the  fixed  stars,  and  the  applicability  of  the 
First  Law  to  it  depends  therefore  on  whether  we  are  dealing  with  its 
motion  relatively  to  the  earth  or  not.  For  most  terrestrial  motions 
it  is  sufficient  to  regard  the  Laws  of  Motion  as  referring  to  motion 
relative  to  the  earth  ;  or,  in  other  words,  we  may  for  this  purpose 
treat  the  earth  as  "  fixed.''  But  if  we  examine  certain  terrestrial 
motions  more  exactly,  we  find  that  the  Laws  of  Motion  thus  interpreted 
are  not  quite  true  ;  but  that  we  get  a  more  accurate  explanation  of 
the  observed  phenomena  if  we  regard  the  Laws  of  Motion  as  referring 
to  motion  relative  to  the  centre  of  the  sun  and  to  lines  drawn  from  it 
to  the  stars;  or,  in  other  words,  we  treat  the  centre  of  the  sun  as  a 
"  fixed  "  point  and  these  lines  as  "  fixed  "  directions.  But  again  when 
we  are  dealing  with  the  solar  system  generally  this  interpretation  is 
slightly  inaccurate,  and  we  have  to  treat  the  centre  of  gravity  of  the 
solar  system  instead  of  the  sun  as  "  fixed." 

From  this  point  of  view  we  may  say  that  Newton's  object  in  the 
Principia  was  to  shew  that  it  was  possible  to  choose  a  certain  point 
(the  centre  of  gravity  of  the  solar  system)  and  certain  directions 
(lines  joining  this  point  to  the  fixed  stars),  as  a  base  of  reference, 
such  that  all  motions  being  treated  as  relative  to  this  base,  the  Laws 
of  Motion  and  the  law  of  gravitation  afford  a  consistent  explanation 
of  the  obsei  ved  motions  of  the  bodies  of  the  solar  system. 


234 


A  Short  History  of  Astronomy 


[CH.    IX. 


pole  B  from  the  centre  of  the  earth  o,  then  the  actual 
surface  of  the  earth  extends  at  the  equator  beyond  this 
circle  as  far  as  A,  where,  according  to  Newton,  a  A  is  about 
2^-3  of  o  B  or  o  A,  and  according  to  modern  estimates,  based 
on  actual  measurement  of  the  earth  as  well  as  upon  theory 
(chapter  x.,  §  221),  it  is  about  -^^  of  o  A.  Both  Newton's 
fraction  and  the  modern  one  are  so  small  that  the  resulting 
flattening  cannot  be  made  sensible  in  a  figure;  in  fig.  72 


FIG.  72. — The  spheroidal  form  of  the  earth. 

the  length  a  A  is  made,  for  the  sake  of  distinctness,  nearly 
30  times  as  great  as  it  should  be. 

Newton  discovered  also  in  a  similar  way  the  flattening 
of  Jupiter,  which,  owing  to  its  more  rapid  rotation,  is 
considerably  more  flattened  than  the  earth  ;  this  was  also 
detected  telescopically  by  Domenico  Cassini  four  years 
after  the  publication  of  the  Principia. 

1 88.  The  discovery  of  the  form  of  the  earth  led  to 
an  explanation  of  the  precession  of  the  equinoxes,  a 
phenomenon  which  had  been  discovered  i, 800  years  before 


$$  :83,  189]      The  Shape  of  the  Earth :  Precession  235 

(chapter  n.,  §  42),  but  had  remained  a  complete  mystery 
ever  since. 

If  the  earth  is  a  perfect  sphere,  then  its  attraction  on 
any  other  body  is  exactly  the  same  as  if  its  mass  were  all 
concentrated  at  its  centre  (§  182),  and  so  also  the  attraction 
on  it  of  any  other  body  such  as  the  sun  or  moon  is 
equivalent  to  a  single  force  passing  through  the  centre  o  of 
the  earth  ;  but  this  is  no  longer  true  if  the  earth  is  not 
spherical.  In  fact  the  action  of  the  sun  or  moon  on  the 
spherical  part  of  the  earth,  inside  the  dotted  circle  in 
fig.  72,  is  equivalent  to  a  force  through  o,  and  has  no 
tendency  to  turn  the  earth  in  any  way  about  its  centre ; 
but  the  attraction  on  the  remaining  portion  is  of  a  different 
character,  and  Newton  shewed  that  from  it  resulted  a 
motion  of  the  axis  of  the  earth  of  the  same  general 
character  as  precession.  The  amount  of  the  precession  as 
calculated  by  Newton  did  as  a  matter  of  fact  agree  pretty 
closely  with  the  observed  amount,  but  this  was  due  to  the 
accidental  compensation  of  two  errors,  arising  from  his 
imperfect  knowledge  of  the  form  and  construction  of  the 
earth,  as  well  as  from  erroneous  estimates  of  the  distance 
of  the  sun  and  of  the  mass  of  the  moon,  neither  of  which 
quantities  Newton  was  able  to  measure  with  any  accuracy.* 
It  was  further  pointed  out  that  the  motion  in  question  was 
necessarily  not  quite  uniform,  but  that,  owing  to  the  unequal 
effects  of  the  sun  in  different  positions,  the  earth's  axis 
would  oscillate  to  and  fro  every  six  months,  though  to  a' 
very  minute  extent. 

189.  Newton  also  gave  a  general  explanation  of  the  tides 
as  due  to  the  disturbing  action  of  the  moon  and  sun,  the 
former  being  the  more  important.  If  the  earth  be  regarded 
as  made  of  a  solid  spherical  nucleus,  covered  by  the  ocean, 
then  the  moon  attracts  different  parts  unequally,  and  in 
particular  the  attraction,  measured  by  the  acceleration  pro- 
duced, on  the  water  nearest  to  the  moon  is  greater  than 

*  He  estimated  the  annual  precession  due  to  the  sun  to  be  about 
9",  and  that  due  to  the  moon  to  be  about  four  and  a  half  times  as 
great,  so  that  the  total  amount  due  to  the  two  bodies  came  out  about 
50",  which  agrees  within  a  fraction  of  a  second  with  the  amount 
shewn  by  observation  ;  but  we  know  now  that  the  moon's  share  is 
not  much  more  than  twice  that  of  the  sun. 


236  A  Short  History  of  Astronomy  [CM.  IX. 

that  on  the  solid  earth,  and  that  on  the  water  farthest  from 
the  moon  is  less.  Consequently  the  water  m<>ves  on  the 
surface  of  the  earth,  the  general  character  of  the  motion 
being  the  same  as  if  the  portion  of  the  ocean  on  the  side 
towards  the  moon  were  attracted  and  that  on  the  opposite 
side  repelled.  Owing  to  the  rotation  of  the  earth  and 
the  moon's  motion,  the  moon  returns  to  nearly  the 
same  position  with  respect  to  any  place  on  the  earth  in 
a  period  which  exceeds  a  day  by  (on  the  average)  about  50 
minutes,  and  consequently  Newton's  argument  shewed 
that  low  tides  (or  high  tides)  due  to  the  moon  would  follow 
one  another  at  any  given  place  at  intervals  equal  to  about 
half  this  period ;  or,  in  other  words,  that  two  tides  would 
in  general  occur  daily,  but  that  on  each  day  any  particular 
phase  of  the  tides  would  occur  on  the  average  about  50 
minutes  later  than  on  the  preceding  day,  a  result  agreeing 
with  observation.  Similar  but  smaller  tides  were  shewn 
by  the  same  argument  to  arise  from  the  action  of  the 
sun,  and  the  actual  tide  to  be  due  to  the  combination  of 
the  two.  It  was  shewn  that  at  new  and  full  moon  the 
lunar  and  solar  tides  would  be  added  together,  whereas 
at  the  half  moon  they  would  tend  to  counteract  one  another, 
so  that  the  observed  fact  of  greater  tides  every  fortnight 
received  an  explanation.  A  number  of  other  peculiarities 
of  the  tides  were  also  shewn  to  result  from  the  same 
principles. 

Newton  ingeniously  used  observations  of  the  height  of 
the  tide  when  the  sun  and  moon  acted  together  and 
when  they  acted  in  opposite  ways  to  compare  the  tide- 
raising  powers  of  the  sun  and  moon,  and  hence  to  estimate 
the  mass  of  the  moon  in  terms  of  that  of  the  sun,  and 
consequently  in  terms  of  that  of  the  earth  (§  185).  The 
resulting  mass  of  the  moon  was  about  twice  what  it  ought 
to  be  according  to  modern  knowledge,  but  as  before 
Newton's  time  no  one  knew  of  any  method  of  measuring 
the  moon's  mass  even  in  the  roughest  way,  and  this  result 
had  to  be  disentangled  from  the  innumerable  complications 
connected  with  both  the  theory  and  with  observation  of 
the  tides,  it  cannot  but  be  regarded  as  a  remarkable  achieve- 
ment. Newton's  theory  of  the  tides  was  based  on  certain 
hypotheses  which  had  to  be  made  in  order  to  render  the 


§  1 90]  Tides  and  Comets  237 

problem  at  all  manageable,  but  which  were  certainly  not 
true,  and  consequently,  as  he  was  well  aware,  important 
modifications  would  necessarily  have  to  be  made,  in  order 
to  bring  his  results  into  agreement  with  actual  facts.  The 
mere  presence  of  land  not  covered  by  water  is,  for  example, 
sufficient  by  itself  to  produce  important  alterations  in  tidal 
effects  at  different  places.  Thus  Newton's  theory  was  bys 
no  means  equal  to  such  a  task  as  that  of  predicting  the 
times  of  high  tide  at  any  required  place,  or  the  height  of 
any  required  tide,  though  it  gave  a  satisfactory  explanation 
of  many  of  the  general  characteristics  of  tides. 

190.  As  we  have  seen  (chapter  v.,  §  103;  chapter  vii., 
§  146),  comets  until  quite  recently  had  been  commonly 
regarded  as  terrestrial  objects  produced  in  the  higher 
regions  of  our  atmosphere,  and  even  the  more  enlightened 
astronomers  who,  like  Tycho,  Kepler,  and  Galilei,  recog- 
nised them  as  belonging  to  the  celestial  bodies,  were  un- 
able to  give  an  explanation  of  their  motions  and  of  their 
apparently  quite  irregular  appearances  and  disappearances. 
Newton  was  led  to  consider  whether  a  comet's  motion 
could  not  be  explained,  like  that  of  a  planet,  by  gravitation 
towards  the  sun.  If  so  then,  as  he  had  proved  near  the 
beginning  of  the  Principia,  its  path  must  be  either  an  ellipse 
or  one  of  two  other  allied  curves,  the  parabola  and 
hyperbola.  If  a  comet  moved  in  an  ellipse  which  only 
differed  slightly  from  a  circle,  then  it  would  never  recede 
to  any  very  great  distance  from  the  centre  of  the  solar 
system,  and  would  therefore  be  regularly  visible,  a  result 
which  was  contrary  to  observation.  If,  however,  the  ellipse 
was  very  elongated,  as  shewn  in  fig.  73,  then  the  period 
of  revolution  might  easily  be  very  great,  and,  during  the 
greater  part  of  it,  the  comet  would  be  so  far  from  the  sun 
and  consequently  also  from  the  earth  as  to  be  invisible. 
If  so  the  comet  would  be  seen  for  a  short  time  and  become 
invisible,  only  to  reappear  after  a  very  long  time,  when 
it  would  naturally  be  regarded  as  a  new  comet.  If  again 
the  path  of  the  comet  were  a  parabola  (which  may  be 
regarded  as  an  ellipse  indefinitely  elongated),  the  comet 
would  not  return  at  all,  but  would  merely  be  seen  once 
when  in  that  part  of  its  path  which  is  near  the  sun.  But 
if  a  comet  moved  in  a  parabola,  with  the  sun  in  a  focus, 


238  A  Short  History  of  Astronomy  [CH.  IX. 

then  its  positions  when  not  very  far  from  the  sun  would 
be  almost  the  same  as  if  it  moved  in  an  elongated  ellipse 
(see  fig.  73),  and  consequently  it  would  hardly  be  possible 
to  distinguish  the  two  cases.  Newton  accordingly  worked 
out  the  case  of  motion  in  a  parabola,  which  is  mathemati- 
cally the  simpler,  and  found  that,  in  the  case  of  a  comet 
which  had  attracted  much  attention  in  the  winter  1680-1, 
a  parabolic  path  could  be  found,  the  calculated  places  of 
the  comet  in  which  agreed  closely  with  those  observed. 
In  the  later  editions  of  the  Principia  the  motions  of  a 
number  of  other  comets  were  investigated  with  a  similar 


FIG.  73. — An  elongated  ellipse  and  a  parabola. 

result.  It  was  thus  established  that  in  many  cases  a 
comet's  path  is  either  a  parabola  or  an  elongated  ellipse, 
and  that  a  similar  result  was  to  be  expected  in  other  cases. 
This  reduction  to  rule  of  the  apparently  arbitrary  motions 
of  comets,  and  their  inclusion  with  the  planets  in  the  same 
class  of  bodies  moving  round  the  sun  under  the  action 
of  gravitation,  may  fairly  be  regarded  as  one  of  the  most 
striking  of  the  innumerable  discoveries  contained  in  the 
Principia. 

In  the  same  section  Newton  discussed  also  at  some 
length  the  nature  of  comets  and  in  particular  the  structure 
of  their  tails,  arriving  at  the  conclusion,  which  is  in  general 
agreement  with  modern  theories  (chapter  XIIL,  §  304),  that 


igi]  Comets  :  Reception  of  the  Principia  239 

the  tail  is  formed  by  a  stream  of  finely  divided  matter 
of  the  nature  of  smoke,  rising  up  from  the  body  of  the 
comet,  and  so  illuminated  by  the  light  of  the  sun  when 
tolerably  near  it'  as  to  become  visible. 

191.  The  Principia  was  published,  as  we  have  seen,  in 
1687.  Only  a  small  edition  seems  to  have  been  printed, 
and  this  was  exhausted  in  three  or  four  years.  Newton's 
earlier  discoveries,  and  the  presentation  to  the  Royal 
Society  of  the  tract  De  Motu  (§  177),  had  prepared  the 
scientific  world  to  look  for  important  new  results  in  t^2 
Principia^  and  the  book  appears  to  have  been  read  by 
the  leading  Continental  mathematicians  and  astronomers, 
and  to  have  been  very  warmly  received  in  England.  The 
Cartesian  philosophy  had,  however,  too  firm  a  hold  to  be 
easily  shaken ;  and  Newton's  fundamental  principle,  in- 
volving as  it  did  the  idea  of  an  action  between  two  bodies 
separated  by  an  interval  of  empty  space,  seemed  impossible 
of  acceptance  to  thinkers  who  had  not  yet  fully  grasped 
the  notion  of  judging  a  scientific  theory  by  the  extent 
to  which  its  consequences  agree  with  observed  facts. 
Hence  even  so  able  a  man  as  Huygens  (chapter  vin., 
§§  154,  157,  158),  regarded  the  idea  of  gravitation  as 
"  absurd,"  and  expressed  his  surprise  that  Newton  should 
have  taken  the  trouble  to  make  such  a  number  of  laborious 
calculations  with  no  foundation  but  this  principle,  a  remark 
which  shewed  Huygens  to  have  had  no  conception  that 
the  agreement  of  the  results  of  these  calculations  with 
actual  facts  was  proof  of  the  soundness  of  the  principle. 
Personal  reasons  also  contributed  to  the  Continental  neglect 
of  Newton's  work,  as  the  famous  quarrel  between  Newton 
and  Leibniz  as  to  their  respective  claims  to  the  invention 
of  what  Newton  called  fluxions  and  Leibniz  the  differen- 
tial method  (out  of  which  the  differential  and  integral 
calculus  have  developed)  grew  in  intensity  and  fresh  com- 
batants were  drawn  into  it  on  both  sides.  Half  a  century 
in  fact  elapsed  before  Newton's  views  made  any  substantial 
progress  on  the  Continent  (cf.  chapter  XL,  §  229).  In  our 
country  the  case  was  different ;  not  only  was  the  Prindpia 
read  with  admiration  by  the  few  who  were  capable  of 
understanding  it,  but  scholars  like  Bentley,  philosophers 
like  Locke,  and  courtiers  like  Halifax  all  made  attempts 


240  A  Short  History  of  Astronomy  [CH.  IX. 

to  grasp  Newton's  general  ideas,  even  though  the  details 
of  his  mathematics  were  out  of  their  range.  It  was  more- 
over soon  discovered  that  his  scientific  ideas  could  be 
used  with  advantage  as  theological  argument?- 

192.  One  unfortunate  result  of  the  great  success  of  the 
Prindpia  was  that  Newton  was  changed  from  a  quiet 
Cambridge  professor,  with  abundant  leisure  and  a  slender 
income,  into  a  public  character,  with  a  continually  increas- 
ing portion  of  his  time  devoted  to  public  business  of  one 
sort  or  another. 

**  Just  before  the  publication  of  the  Prindpia  he  had  been 
appointed  one  of  the  representatives  of  his  University  to 
defend  its  rights  against  the  encroachments  of  James  II., 
and  two  years  later  he  sat  as  member  for  the  University 
in  the  Convention  Parliament,  though  he  retired  after  its 
dissolution. 

Notwithstanding  these  and  many  other  distractions,  he 
continued  to  work  at  the  theory  of  gravitation,  paying 
particular  attention  to  the  lunar  theory,  a  difficult  subject 
with  his  treatment  of  which  he  was  never  quite  satisfied.* 
He  was  fortunately  able  to  obtain  from  time  to  time  first- 
rate  observations  of  the  moon  (as  well  as  of  other  bodies) 
from  the  Astronomer  Royal  Flamsteed  (chapter  x.,  §§  197-8), 
though  Newton's  continual  requests  and  Flamsteed's  occa- 
sional refusals  led  to  strained  relations  at  intervals.  It  is 
possible  that  about  this  time  Newton  contemplated  writing 
a  new  treatise,  with  more  detailed  treatment  of  various 
•points  discussed  in  the  Prindpia;  and  in  1691  there  was 
already  some  talk  of  a  new  edition  of  the  Prindpia,  possibly 
to  be  edited  by  some  younger  mathematician.  In  any 
case  nothing  serious  in  this  direction  was  done  for  some 
years,  perhaps  owing  to  a  serious  illness,  apparently  some 
nervous  disorder,  which  attacked  Newton  in  1692  and 
lasted  about  two  years.  During  this  illness,  as  he  himself 
said,  "  he  had  not  his  usual  consistency  of  mind,"  and  it  is 
by  no  means  certain  that  he  ever  recovered  his  full  mental 
activity  and  power. 

Soon  after  recovering  from  this  illness  he  made  some 

*  He  once  told  Halley  in  despair  that  the  lunar  theory  '  made 
his  head  ache  and  kept  him  awake  so  often  that  he  would  think  oi 
it  no  more." 


NEWTON. 


[To  face  p.  24c 


§§  i92,  193]  Newtorfs  Later  Life  241 

preparations  for  a  new  edition  of  the  Principia,  besides 
going  on  with  the  lunar  theory,  but  the  work  was  again 
interrupted  in  1695,  when  he  received  the  valuable  appoint- 
ment of  Warden  to  the  Mint,  from  which  he  was  promoted 
to  the  Mastership  four  years  later.  He  had,  in  conse- 
quence, to  move  to  London  (1696),  and  much  of  his  time 
was  henceforward  occupied  by  official  duties.  In  1701 
he  resigned  his  professorship  at  Cambridge,  and  in  the 
same  year  was  for  the  second  time  elected  the  Parliamentary 
representative  of  the  University.  In  1703  he  was  chosen 
President  of  the  Royal  Society,  an  office  which  he  held  till 
his  death,  and  in  1705  he  was  knighted  on  the  occasion  of 
a  royal  visit  to  Cambridge. 

During  this  time  he  published  (1704)  his  treatise  on 
Optics,  the  bulk  of  which  was  probably  written  long  before, 
and  in  1709  he  finally  abandoned  the  idea  of  editing  the 
Prindpia  himself,  and  arranged  for  the  work  to  be  done  by 
Roger  Cotes  (1682-1716),  the  brilliant  young  mathematician 
whose  untimely  death  a  few  years  later  called  from  Newton 
the  famous  eulogy,  "  If  Mr.  Cotes  had  lived  we  might 
have  known  something."  The  alterations  to  be  made  were 
discussed  in  a  long  and  active  correspondence  between  the 
editor  and  author,  the  most  important  changes  being 
improvements  and  additions  to  the  lunar  theory,  and  to 
the  discussions  of  precession  and  of  comets,  though  there 
were  also  a  very  large  number  of  minor  changes ;  and  the 
new  edition  appeared  in  1713.  A  third  edition,  edited  by 
Pemberton,  was  published  in  1726,  but  this  time  Newton, 
who  was  over  80,  took  much  less  part,  and  the  alterations 
were  of  no  great  importance.  This  was  Newton's  last  piece 
of  scientific  work,  and  his  death  occurred  in  the  following 
year  (March  3rd,  1727). 

193.  It  is  impossible  to  give  an  adequate  idea  of  the 
immense  magnitude  of  Newton's  scientific  discoveries 
except  by  a  free  use  of  the  mathematical  technicalities  in 
which  the  bulk  of  them  were  expressed.  The  criticism 
passed  on  him  by  his  personal  enemy  Leibniz  that, 
"Taking  mathematics  from  the  beginning  of  the  world 
to  the  time  when  Newton  lived,  what  he  had  done  was 
much  the  better  half,"  and  the  remark  of  his  great  suc- 
cessor Lagrange  (chapter  XL,  §  237),  "  Newton  was  the 

16 


242  A  Short  History  of  Astronomy  [CH.  ix. 

greatest  genius  that  ever  existed,  and  the  most  fortunate, 
for  we  cannot  find  more  than  once  a  system  of  the  world 
to  establish,"  shew  the  immense  respect  for  his  work  felt 
by  those  who  were  most  competent  to  judge  it. 

With  these  magnificent  eulogies  it  is  pleasant  to  compare 
Newton's  own  grateful  recognition  of  his  predecessors, 
"  If  I  have  seen  further  than  other  men,  it  is  because  I 
have  stood  upon  the  shoulders  of  the  giants,"  and  his 
modest  estimate  of  his  own  performances  :— 

"I  do  not  know  what  I  may  appear  to  the  world  ;  but  to 
myself  I  seem  to  have  been  only  like  a  boy  playing  on  the  sea- 
shore, and  diverting  myself  in  now  and  then  finding  a  smoother 
pebble  or  a  prettier  shell  than  ordinary,  whilst  the  great  ocean 
of  truth  lay  all  undiscovered  before  me." 

194.  It  is  sometimes  said,  in  explanation  of  the  differ- 
ence between  Newton's  achievements  and  those  of  earlier 
astronomers,  that  whereas  they  discovered  how  the  celestial 
bodies  moved,  he  shewed  why  the  motions  were  as  they 
were,  or,  in  other  words,  that  they  described  motions  while 
he  explained  them  or  ascertained  their  cause.  It  is, 
however,  doubtful  whether  this  distinction  between  How 
and  Why,  though  undoubtedly  to  some  extent  convenient, 
has  any  real  validity.  Ptolemy,  for  example,  represented 
the  motion  of  a  planet  by  a  certain  combination  of  epi- 
cycles ;  his  scheme  was  equivalent  to  a  particular  method 
of  describing  the  motion  ;  but  if  any  one  had  asked  him 
why  the  planet  would  be  in  a  particular  position  at  a 
particular  time,  he  might  legitimately  have  answered  that 
it  was  so  because  the  planet  was  connected  with  this  par- 
ticular system  of  epicycles,  and  its  place  could  be  deduced 
from  them  by  a  rigorous  process  of  calculation.  But  if 
any  one  had  gone  further  and  asked  why  the  planet's 
epicycles  were  as  they  were,  Ptolemy  could  have  given  no 
answer.  Moreover,  as  the  system  of  epicycles  differed  in 
some  important  respects  from  planet  to  planet,  Ptolemy's 
system  left  unanswered  a  number  of  questions  which 
obviously  presented  themselves.  Then  Coppernicus  gave 
a  partial  answer  to  some  of  these  questions.  To  the 
question  why  certain  of  the  planetary  motions,  correspond- 
ing to  certain  epicycles,  existed,  he  would  have  replied  that 
it  was  because  of  certain  motion?  cf  the  earth,  from  which 


§•  194]  Explanation  and  Description  243 

these  (apparent)  planetary  motions  could  be  deduced  as 
necessary  consequences.  But  the  same  information  could 
also  have  been  given  as  a  mere  descriptive  statement  that 
the  earth  moves  in  certain  ways  and  the  planets  move  in 
certain  other  ways.  But  again,  if  Coppernicus  had  been 
asked  why  the  earth  rotated  on  its  axis,  or  why  the  planets 
revolved  round  the  sun,  he  could  have  given  no  answer; 
still  less  could  he  have  said  why  the  planets  had  certain 
irregularities  in  their  motions,  represented  by  his  epicycles. 

Kepler  again  described  the  same  motions  very  much 
more  simply  and  shortly  by  means  of  his  three  laws  of 
planetary  motion ;  but  if  any  one  had  asked  why  a  planet's 
motion  varied  in  certain  ways,  he  might  have  replied  th.,i 
it  was  because  all  planets  moved  in  ellipses  so  as  to  sweep 
out  equal  areas  in  equal  times.  Why  this  was  so  Kepler 
was  unable  to  say,  though  he  spent  much  time  in  specu- 
lating on  the  subject.  This  question  was,  however,  answered 
by  Newton,  who  shewed  that  the  planetary  motions  were 
necessary  consequences  of  his  law  of  gravitation  and  his 
laws  of  motion.  Moreover  from  these  same  laws,  which 
were  extremely  simple  in  statement  and  few  in  number, 
followed  as  necessary  consequences  the  motion  of  the 
moon  and  many  other  astronomical  phenomena,  and  also 
certain  familiar  terrestrial  phenomena,  such  as  the  behaviour 
of  falling  bodies ;  so  that  a  large  number  of  groups  of 
observed  facts,  which  had  hitherto  been  disconnected  from 
one  another,  were  here  brought  into  connection  as  neces- 
sary consequences  of  certain  fundamental  laws.  But  again 
Newton's  view  of  the  solar  system  might  equally  well  be 
put  as  a  mere  descriptive  statement  that  the  planets,  etc., 
move  with  accelerations  of  certain  magnitudes  towards  one 
rmother.  As,  however,  the  actual  position  or  rate  of  motion 
of  a  planet  at  any  time  can  only  be  deduced  by  an  extremely 
elaborate  calculation  from  Newton's  laws,  they  are  not  at 
all  obviously  equivalent  to  the  observed  celestial  motions, 
and  we  do  not  therefore  at  all  easily  think  of  them  as  being 
merely  a  description. 

Again  Newton's  laws  at  once  suggest  the  question  why 
bodies  attract  one  another  in  this  particular  way ;  and  this 
question,  which  Newton  fully  recognised  as  legitimate,  he 
was  unable  to  answer.  Or  again  we  might  ask  why  the 


244  A  Short  History  of  Astronomy  [CH.  ix. 

planets  are  of  certain  sizes,  at  certain  distances  from  the 
sun,  etc.,  and  to  these  questions  again  Newton  could  give 
no  answer. 

But  whereas  the  questions  left  unanswered  by  Ptolemy, 
Coppernicus,  and  Kepler  were  in  whole  or  in  part  answered 
by  their  successors,  that  is,  their  unexplained  facts  or 
laws  were  shewn  to  be  necessary  consequences  of  other 
simpler  and  more  general  laws,  it  happens  that  up  to  the 
present  day  no  one  has  been  able  to  answer,  in  any  satis- 
factory way,  these  questions  which  Newton  left  unanswered. 
In  this  particular  direction,  therefore,  Newton's  laws  mark 
the  boundary  of  our  present  knowledge.  But  if  any  one 
were  to  succeed  this  year  or  next  in  shewing  gravitation  to 
be  a  consequence  of  some  still  more  general  law,  this  new 
law  would  still  bring  with  it  a  new  Why. 

If,  however,  Newton's  laws  cannot  be  regarded  as  an 
ultimate  explanation  of  the  phenomena  of  the  solar  system, 
except  in  the  historic  sense  that  they  have  not  yet  been 
shewn  to  depend  on  other  more  fundamental  laws,  their 
success  in  "  explaining,"  with  fair  accuracy,  such  an  immense 
mass  of  observed  results  in  all  parts  of  the  solar  system, 
and  their  universal  character,  gave  a  powerful  impetus  to 
the  idea  of  accounting  for  observed  facts  in  other  depart- 
ments of  science,  such  as  chemistry  and  physics,  in  some 
similar  way  as  the  consequence  of  forces  acting  between 
bodies,  and  hence  to  the  conception  of  the  material  universe 
as  made  up  of  a  certain  number  of  bodies,  each  acting  on 
one  another  with  definite  forces  in  such  a  way  that  all  the 
changes  which  can  be  observed  to  go  on  are  necessary 
consequences  of  these  forces,  and  are  capable  of  prediction 
by  any  one  who  has  sufficient  knowledge  of  the  forces  and 
sufficient  mathematical  skill  to  develop  their  consequences. 

Whether  this  conception  of  the  material  universe  is 
adequate  or  not,  it  has  undoubtedly  exercised  a  very 
important  influence  on  scientific  discovery  as  well  as  on 
philosophical  thought,  and  although  it  was  never  formulated 
by  Newton,  and  parts  of  it  would  probably  have  been 
repudiated  by  him,  there  are  indications  that  some  such 
ideas  were  in  his  head,  and  those  who  held  the  conception 
most  firmly  undoubtedly  derived  their  ideas  directly  or 
indirectly  from  him. 


$  i9s]  Newton's  Scientific ,  Method  245 

195.  Newton's  scientific  method  did  not  differ  essentially 
from  that  followed  by  Galilei  (chapter  vi.,  §  134),  which 
has  been  variously  described  as  complete  induction  or 
as  the  inverse  deductive  method,  the  difference  in  name 
corresponding  to  a  difference  in  the  stress  laid  upon 
different  parts  of  the  same  general  process.  Facts  are 
obtained  by  observation  or  experiment ;  a  hypothesis  or 
provisional  theory  is  devised  to  account  for  them ;  from 
this  theory  are  obtained,  if  possible  by  a  rigorous  process 
of  deductive  reasoning,  certain  consequences  capable  of 
being  compared  with  actual  facts,  and  the  comparison  is 
then  made.  In  some  cases  the  first  process  may  appear 
as  the  more  important,  but  in  Newton's  work  the  really 
convincing  part  of  the  proof  of  his  results  lay  in  the 
verification  involved  in  the  two  last  processes.  This  has 
perhaps  been  somewhat  obscured  by  his  famous  remark, 
Hypotheses  nonfingo  (I  do  not  invent  hypotheses),  dissociated 
from  its  context.  The  words  occur  in  the  conclusion  of 
the  Principia,  after  he  has  been  speaking  of  universal 
gravitation  : — 

"  I  have  not  yet  been  able  to  deduce  (deducere}  from 
phenomena  the  reason  of  these  properties  of  gravitation,  and 
I  do  not  invent  hypotheses.  For  any  thing  which  cannot  be 
deduced  from  phenomena  should  be  called  a  hypothesis." 

Newton  probably  had  in  his  mind  such  speculations  as 
the  Cartesian  vortices,  which  could  not  be  deduced  directly 
from  observations,  and  the  consequences  of  which  either 
could  not  l)e  worked  out  and  compared  with  actual  facts 
or  were  inconsistent  with  them.  Newton  in  fact  rejected 
hypotheses  which  were  unverifiable,  but  he  constantly  made 
hypotheses,  suggested  by  observed  facts,  and  verified  by 
the  agreement  of  their  consequences  with  fresh  observed 
facts.  The  extension  of  gravity  to  the  moon  (§  173)  is  a 
good  example  :  he  was  acquainted  with  certain  facts  as  to 
the  motion  of  falling  bodies  and  the  motion  of  the  moon  ; 
it  occurred  to  him  that  the  earth's  attraction  might  extend 
as  far  as  the  moon,  and  certain  other  facts  connected  with 
Kepler's  Third  Law  suggested  the  law  of  the  inverse 
square.  If  this  were  right,  the  moon's  acceleration  towards 
the  earth  ought  to  have  a  certain  value,  which  coul  1  b-j 


246  A  Short  History  of  Astronomy      [Cn.  ix.,  §  195 

obtained  by  calculation.  The  calculation  was  made  and 
found  to  agree  roughly  with  the  actual  motion  of  the 
moon. 

Moreover  it  may  be  fairly  urged,  in  illustration  of  the 
great  importance  of  the  process  of  verification,  that 
Newton's  fundamental  laws  were  not  rigorously  established 
by  him,  but  that  the  deficiencies  in  his  proofs  have 
been  to  a  great  extent  filled  up  by  the  elaborate  pro- 
cess of  verification  that  has  gone  on  since.  For  the 
motions  of  the  solar  system,  as  deduced  by  Newton  from 
gravitation  and  the  laws  of  motion,  only  agreed  roughly 
with  observation ;  many  outstanding  discrepancies  were 
left ;  and  though  there  was  a  strong  presumption  that 
these  were  due  to  the  necessary  imperfections  of  Newton's 
processes  of  calculation,  an  immense  expenditure  of  labour 
and  ingenuity  on  the  part  of  a  series  of  mathematicians  has 
been  required  to  remove  these  discrepancies  one  by  one, 
and  as  a  matter  of  fact  there  remain  even  to-day  a  few 
small  ones  which  are  unexplained  (chapter  xin.,  §  290). 


CHAPTER    X. 

OBSERVATIONAL    ASTRONOMY    IN    THE    l8TH    CENTURY. 

"Through  Newton  theory  had  made  a  great  advance  and  was 
ahead  of  observation;  the  latter  now  made  efforts  to  come  once 
more  level  with  theory." — BESSEL. 

196.  NEWTON  virtually  created  a  new  department  of 
astronomy,  gravitational  astronomy,  as  it  is  often  called, 
and  bequeathed  to  his  successors  the  problem  of  deducing 
more  fully  than  he  had  succeeded  in  doing  the  motions  of 
the  celestial  bodies  from  their  mutual  gravitation. 

To  the  solution  of  this  problem  Newton's  own  country- 
men contributed  next  to  nothing  throughout  the  i8th 
century,  and  his  true  successors  were  a  group  of  Continental 
mathematicians  whose  work  began  soon  after  his  death, 
though  not  till  nearly  half  a  century  after  the  publication 
of  the  Prindpia. 

This  failure  of  the  British  mathematicians  to  develop 
Newton's  discoveries  may  be  explained  as  due  in  part  to 
the  absence  or  scarcity  of  men  of  real  ability,  but  in  part 
also  to  the  peculiarity  of  the  mathematical  form  in  which 
Newton  presented  his  discoveries.  The  Prindpia  is  written 
almost  entirely  in  the  language  of  geometry,  modified  in 
a  special  way  to  meet  the  requirements  of  the  case ;  nearly 
all  subsequent  progress  in  gravitational  astronomy  has 
been  made  by  mathematical  methods  known  as  analysis. 
Although  the  distinction  between  the  two  methods  cannot 
be  fully  appreciated  except  by  those  who  have  used  them 
both,  it  may  perhaps  convey  some  impression  of  the  differ- 
ences between  them  to  say  that  in  the  geometrical  treatment 
of  an  astronomical  problem  each  step  of  the  reasoning  is 

247 


248  A  Short  History  of  Astronomy  [Cn.  x. 

expressed  in  such  a  way  as  to  be  capable  of  being  inter- 
preted in  terms  of  the  original  problem,  whereas  in  the 
analytical  treatment  the  problem  is  first  expressed  by 
means  of  algebraical  symbols ;  these  symbols  are  manipulated 
according  to  certain  purely  formal  rules,  no  regard  being 
paid  to  the  interpretation  of  the  intermediate  steps,  and 
the  final  algebraical  result,  if  it  can  be  obtained,  yields  on 
interpretation  the  solution  of  the  original  problem.  The 
geometrical  solution  of  a  problem,  if  it  can  be  obtained, 
is  frequently  shorter,  clearer,  and  more  elegant ;  but,  on 
the  other  hand,  each  special  problem  has  to  be  considered 
separately,  whereas  the  analytical  solution  can  be  con- 
ducted to  a  great  extent  according  to  fixed  rules  applicable 
in  a  larger  number  of  cases.  In  Newton's  time  modern 
analysis  was  only  just  coming  into  being,  some  of  the  most 
important  parts  of  it  being  in  fact  the  creation  of  Leibniz 
and  himself,  and  although  he  sometimes  used  analysis  to 
solve  an  astronomical  problem,  it  was  his  practice  to  translate 
the  result  into  geometrical  language  before  publication  ;  in 
doing  so  he  was  probably  influenced  to  a  large  extent  by 
a  personal  preference  for  the  elegance  of  geometrical  proofs, 
partly  also  by  an  unwillingness  to  increase  the  numerous 
difficulties  contained  in  the  Principia>  by  using  mathematical 
methods  which  were  comparatively  unfamiliar.  But  though 
in  the  hands  of  a  master  like  Newton  geometrical  methods 
were  capable  of  producing  astonishing  results,  the  lesser 
men  who  followed  him  were  scarcely  ever  capable  of  using 
his  methods  to  obtain  results  beyond  those  which  he 
himself  had  reached.  Excessive  reverence  for  Newton  and 
all  his  ways,  combined  with  the  estrangement  which  long 
subsisted  between  British  and  foreign  mathematicians,  as 
the  result  of  the  fluxional  controversy  (chapter  ix.,  §  191), 
prevented  the  former  from  using  the  analytical  methods 
which  were  being  rapidly  perfected  by  Leibniz's  pupils  and 
other  Continental  mathematicians.  Our  mathematicians 
remained,  therefore,  almost  isolated  during  the  whole  of  the 
1 8th  century,  and  with  the  exception  of  some  admirable 
work  by  Colin  Maclaurin  (1698-1746),  which  carried 
Newton's  theory  of  the  figure  of  the  earth  a  stage  further, 
nothing  of  importance  was  done  in  our  country  for  nearly 
a  century  after  Newton's  death  to  develop  the  theory  of 


?  iy7]     Continental  Analysis  and  English   Observation    S249 

gravitation  beyond  the  point  at   which   it  was   left   in   the 
JPrincipia. 

In  other  departments  of  astronomy,  however,  important 
progress  was  made  both  during  and  after  Newton's  lifetime, 
and  by  a  curious  inversion,  while  Newton's  ideas  were 
developed  chiefly  by  French  mathematicians,  the  Observa- 
tory of  Paris,  at  which  Picard  and  others  had  done  such 
admirable  work  (chapter  vin.,  §§  160-2),  produced  little  of 
real  importance  for  nearly  a  century  afterwards,  and  a  lar^e 
part  of  the  best  observing  work  of  the  i8th  century  was 
done  by  Newton's  countrymen.  It  will  be  convenient  to 
separate  these  two  departments  of  astronomical  work,  and 
to  deal  in  the  next  chapter  with  the  development  of  the 
theory  of  gravitation. 

197.  The  first  of  the  great  English  observers  was 
Newton's  contemporary  John  Flamsteed,  who  was  born  near 
Derby  in  1646  and  died  at  Greenwich  in  1720.*  Unfor- 
tunately the  character  of  his  work  was  such  that,  marked 
as  it  was  by  no  brilliant  discoveries,  it  is  difficult  to  present 
it  in  an  attractive  form  or  to  give  any  adequate  idea  of 
its  real  extent  and  importance.  He  was  one  of  tho;e 
laborious  and  careful  investigators,  the  results  of  whose 
work  are  invaluable  as  material  for  subsequent  research, 
but  are  not  striking  in  themselves. 

He  made  some  astronomical  observations  while  quite  a 
boy,  and  wrote  several  papers,  of  a  technical  character,  on 
astronomical  subjects,  which  attracted  some  attention.  In 
1675  he  was  appointed  a  member  of  a  Committee  to  report 
on  a  method  for  finding  the  longitude  at  sea  which  had 
been  offered  to  the  Government  by  a  certain  Frenchman 
of  the  name  of  St.  Pierre.  The  Committee,  acting  largely 
on  Flamsteed's  advice,  reported  unfavourably  on  the 
method  in  question,  and  memorialised  Charles  II.  in 
favour  of  founding  a  national  observatory,  in  order  that 
better  knowledge  of  the  celestial  bodies  might  lead  to  a 
satisfactory  method  of  finding  the  longitude,  a  problem 
which  the  rapid  increase  of  English  shipping  rendered  of 
great  practical  importance.  The  King  having  agreed, 
Flamsteed  was  in  the  same  year  appointed  to  the  new 

*  December  3 1st,  1719,  according  to  the  unreformed  calendar  (O.b*) 
then  in  use  in  England. 


250  A  Short  History  of  Astronomy  [CH.  x. 

office  of  Astronomer  Royal,  with  a  salary  of  ^100  a  year, 
and  the  warrant  for  building  an  Observatory  at  Greenwich 
was  signed  on  June  i2th,  1675.  About  a  year  was  occupied 
in  building  it,  and  Flamsteed  took  up  his  residence  there 
and  began  work  in  July  1676,  five  years  after  Cassini 
entered  upon  his  duties  at  the  Observatory  of  Paris 
(chapter  VIIL,  §  160).  The  Greenwich  Observatory  was, 
however,  on  a  very  different  scale  from  the  magnificent 
sister  institution.  The  King  had,  it  is  true,  provided 
Flamsteed  with  a  building  and  a  very  small  salary,  but 
furnished  him  neither  with  instruments  nor  with  an  assist- 
ant. A  few  instruments  he  possessed  already,  a  few  more 
were  given  to  him  by  rich  friends,  and  he  gradually  made 
at  his  own  expense  some  further  instrumental  additions  of 
importance.  Some  years  after  his  appointment  the  Govern- 
ment provided  him  with  "  a  silly,  surly  labourer  "  to  help 
him  with  some  of  the  rough  work,  but  he  was  compelled 
to  provide  more  skilled  assistance  out  of  his  own  pocket, 
and  this  necessity  in  turn  compelled  him  to  devote  some 
part  of  his  valuable  time  to  taking  pupils. 

198.  Flamsteed's  great  work  was  the  construction  of  a 
more  accurate  and  more  extensive  star  catalogue  than  any 
that  existed  ;  he  also  made  a  number  of  observations  ot 
the  moon,  of  the  sun,  and  to  a  less  extent  of  other  bodies. 
Like  Tycho,  the  author  of  the  last  great  star  catalogue 
(chapter  v.,  §  107),  he  found  problems  continually  presenting 
themselves  in  the  course  of  his  work  which  had  to  be 
solved  before  his  main  object  could  be  accomplished,  and 
we  accordingly  owe  to  him  the  invention  of  several  improve- 
ments in  practical  astronomy,  the  best  known  being  his 
method  of  finding  the  position  of  the  first  point  of  Aries 
(chapter  11.,  §  42),  one  of  the  fundamental  points  with 
reference  to  which  all  positions  on  the  celestial  sphere  are 
defined.  He  was  the  first  astronomer  to  use  a  clock 
systematically  for  the  determination  of  one  of  the  two 
fundamental  quantities  (the  right  ascension)  necessary  to 
fix  the  position  of  a  star,  a  method  which  was  first  suggested 
and  to  some  extent  used  by  Picard  (chapter  VIIL,  §  157), 
and,  as  soon  as  he  could  get  the  necessary  instruments, 
he  regularly  used  the  telescopic  sights  of  Gascoigne  and 
Auzout  (chapter  VIIL,  §  155),  instead  of  making  naked-eye 


$  ig8]  Flamsteed  '  251 

observations.  Thus  while  Hevel  (chapter  vin.,  §  153) 
was  the  last  and  most  accurate  observer  of  the  old  school, 
employing  methods  not  differing  essentially  from  those 
which  had  been  in  use  for  centuries,  Flamsteed  belongs 
to  the  new  school,  and  his  methods  differ  rather  in  detail 
than  in  principle  from  those  now  in  vogue  for  similar  work 
at  Greenwich,  Paris,  or  Washington.  This  adoption  of 
new  methods,  together  with  the  most  scrupulous  care  in 
details,  rendered  Flamsteed's  observations  considerably 
more  accurate  than  any  made  in  his  time  or  earlier,  the 
first  definite  advance  afterwards  being  made  by  Bradley 
(§  218). 

Flamsteed  compared  favourably  with  many  observers 
by  not  merely  taking  and  recording  observations,  but  by 
performing  also  the  tedious  process  known  as  reduction 
(§  218),  whereby  the  results  of  the  observation  are  put 
into  a  form  suitable  for  use  by  other  astronomers;  this 
process  is  usually  performed  in  modern  observatories  by 
assistants,  but  in  Flamsteed's  case  had  to  be  done  almost 
exclusively  by  the  astronomer  himself.  From  this  and 
other  causes  he  was  extremely  slow  in  publishing  observa- 
tions;  we  have  already  alluded  (chapter  ix.,  §  192)  to  the 
difficulty  which  Newton  had  in  extracting  lunar  observations 
from  him,  and  after  a  time  a  feeling  that  the  object  for 
which  the  Observatory  had  been  founded  was  not  being  ful- 
filled became  pretty  general  among  astronomers.  Flamsteed 
always  suffered  from  bad  health  as  well  as  from  the 
pecuniary  and  other  difficulties  which  have  been  referred 
to ;  moreover  he  was  much  more  anxious  that  his  observa- 
tions should  be  kept  back  till  they  were  as  accurate  as 
possible,  than  that  they  should  be  published  in  a  less 
perfect  form  and  used  for  the  researches  which  he  once 
called  "  Mr.  Newton's  crotchets " ;  consequently  he  took 
remonstrances  about  the  delay  in  the  publication  of  his 
observations  in  bad  part.  Some  painful  quarrels  occurred 
between  Flamsteed  on  the  one  hand  and  Newton  and 
Halley  on  the  other.  The  last  straw  was  the  unauthorised 
publication  in  1712,  under  the  editorship  of  Halley,  of  a 
volume  of  Flamsteed's  observations,  a  proceeding  to  which 
Flamsteed  not  unnaturally  replied  by  calling  Halley  a 
"malicious  thief."  Three  years  later  he  succeeded  in 


252  A  Short  History  of  Astronomy  [Cn.  x. 

getting  hold  of  all  the  unsold  copies  and  in  destroying 
them,  but  fortunately  he  was  also  stimulated  to  prepare 
for  publication  an  authentic  edition.  The  Historia  Coelestis 
Britannica,  as  he  called  the  book,  contained  an  immense 
series  of  observations  made  both  before  and  during  his 
career  at  Greenwich,  but  the  most  important  and  per- 
manently valuable  part  was  a  catalogue  of  the  places  of 
nearly  3,000  stars.* 

Flamsteed  himself  only  lived  just  long  enough  to  finish 
the  second  of  the  three  volumes  ;  the  third  was  edited 
by  his  assistants  Abraham  Sharp  (1651-1742)  and  Joseph 
Crosthwait ;  and  the  whole  was  published  in  1725.  Four 
years  later  still  appeared  his  valuable  Star-Atlas,  which 
long  remained  in  common  use. 

The  catalogue  was  not  only  three  times  as  extensive  as 
Tycho's,  which  it  virtually  succeeded,  but  was  also  very 
much  more  accurate.  It  has  been  estimated  t  that,  whereas 
Tycho's  determinations  of  the  positions  of  the  stars  were 
on  the  average  about  i'  in  error,  the  corresponding  errors 
in  Flamsteed's  case  were  about  10".  This  quantity  is  the 
apparent  diameter  of  a  shilling  seen  from  a  distance^  of 
about  500  yards ;  so  that  if  two  marks  were  made  at 
opposite  points  on  the  edge  of  the  coin,  and  it  were  placed 
at  a  distance  of  500  yards,  the  two  marks  might  be  taken 
to  represent  the  true  direction  of  an  average  star  and  its 
direction  as  given  in  Flamsteed's  catalogue.  In  some 
cases  of  course  the  error  might  be  much  greater  and  in 
others  considerably  less. 

Flamsteed  contributed  to  astronomy  no  ideas  of  first-rate 
importance  ;  he  had  not  the  ingenuity  of  Picard  and  of 
Roemer  in  devising  instrumental  improvements,  and  he 
took  little  interest  in  the  theoretical  work  of  Newton ;  % 
but  by  unflagging  industry  and  scrupulous  care  he  succeeded 
in  bequeathing  to  his  successors  an  immense  treasure  of 

*  The  apparent  number  is  2,935,  but  12  of  these  are  duplicates. 

f  By  Bessel  (chapter  xin.,  §  277). 

j  The  relation  between  the  work  of  Flamsteed  and  that  of  Newton 
was  expressed  with  more  correctness  than  good  taste  by  the  two 
astronomers  themselves,  in  the  course  of  some  quarrel  about  the 
lunar  theor3'  :  "  Sir  Isaac  worked  with  the  ore  I  had  dug."  "  If  he 
dug  the  ore,  I  made  the  gold  ring." 


$$  i99,  2c0]          Flamsteed' s  Observations:  Halley  253 

observations,  executed  with  all   the  accuracy  that  his   in- 
strumental means  permitted. 

199.  Flamsteed   was   succeeded    as   Astronomer   Royal 
by   Edmund    Halley,   whom   we   have    already   met   with 
(chapter  ix.,  §  176)  as  Newton's  friend  and  helper. 

Born  in  1656,  ten  years  after  Flamsteed,  he  studied 
astronomy  in  his  schooldays,  and  published  a  paper  on  the 
orbits  of  the  planets  as  early  as  1676.  In  the  same  year 
he  set  off  for  St.  Helena  (in  latitude  16°  S.)  in  order  to 
make  observations  of  stars  which  were  too  near  the  south 
pole  to  be  visible  in  Europe.  The  climate  turned  out  to 
be  disappointing,  and  he  was  only  able  after  his  return 
to  publish  (1678)  a  catalogue  of  the  places  of  341  southern 
stars,  which  constituted,  however,  an  important  addition 
to  precise  knowledge  of  the  stars.  The  catalogue  was  also 
remarkable  as  being  the  first  based  on  telescopic  observa- 
tion, though  the  observations  do  not  seem  to  have  been 
taken  with  all  the  accuracy  which  his  instruments  rendered 
attainable.  During  his  stay  at  St.  Helena  he  also  took 
a  number  of  pendulum  observations  which  confirmed  the 
results  obtained  a  few  years  before  by  Richer  at  Cayenne 
(chapter  vin.,  §  16 1),  and  also  observed  a  transit  of  Mercury 
across  the  sun,  which  occurred  in  November  1677. 

After  his  return  to  England  he  took  an  active  part  in 
current  scientific  questions,  particularly  in  those  connected 
with  astronomy,  and  made  several  small  contributions  to 
the  subject.  In  1684,  as  we  have  seen,  he  first  came 
effectively  into  contact  with  Newton,  and  spent  a  good 
part  of  the  next  few  years  in  helping  him  with  the 
Frinripia. 

200.  Of  his  numerous  contributions  to  astronomy,  which 
touched   almost   every   branch    of    the    subject,    his    work 
on    comets    is    the    best    known   and    probably    the   most 
important.     He  observed  the  comets  of  1680  and  1682  ; 
he  worked  out  the  paths  both  of  these  and  of  a  number 
of   other   recorded   comets  in  accordance  with    Newton's 
principles,   and   contributed  a  good  deal  of  the   material 
contained   in  the  sections   of  the  Principia   dealing  wi.h 
cornets,    particularly    in   the    later   editions.     In    1705    he 
published  a  Synopsis  of  Cometary  Astronomy  in  which  no  \ 
less  than  24  cometary  orbits  were  calculated.     Struck  by   1 


254  A  Short  History  of  Astronomy  [Cn.  x. 

the  resemblance  between  the  paths  described  by  the 
comets  of  1531,  1607,  and  1682,  and  by  the  approximate 
equality  in  the  intervals  between  their  respective  appear- 
ances and  that  of  a  fourth  comet  seen  in  1456,  he  was 
shrewd  enough  to  conjecture  that  the  three  later  comets, 
if  not  all  four,  were  really  different  appearances  of  the  same 
comet,  which  revolved  round  the  sun  in  an  elongated 
ellipse  in  a  period  of  about  75  or  76  years.  He  explained 
the  difference  between  the  76  years  which  separate  the 
appearances  of  the  comet  in  1531  and  1607,  and  the  slightly 
shorter  period  which  elapsed  between  1607  and  1682,  as 
probably  due  to  the  perturbations  caused  by  planets  near 
which  the  comet  had  passed  ;  and  finally  predicted  the 
probable  reappearance  of  the  same  comet  (which  now 
deservedly  bears  his  name)  about  76  years  after  its  last 
appearance,  i.e.  about  1758,  though  he  was  again  aware 
that  planetary  perturbation  might  alter  the  time  of  its 
appearance  ;  and  the  actual  appearance  of  the  comet  about 
the  predicted  time  (chapter  XL,  §  231)  marked  an  important 
era  in  the  progress  of  our  knowledge  of  these  extremely 
troublesome  and  erratic  bodies. 

201.  In   1693  Halley  read  before  the  Royal  Society  a 
paper   in  which   he   called   attention   to   the   difficulty  of 
reconciling  certain  ancient  eclipses  with  the  known  motion 
of  the  moon,  and  referred  to  the  possibility  of  some  slight 
increase  in  the  moon's  average  rate  of  motion  round  the 
earth. 

This  irregularity,  now  known  as  the  secular  acceleration 
of  the  moon's  mean  motion,  was  subsequently  more 
definitely  established  as  a  fact  of  observation  ;  and  the 
difficulties  met  with  in  explaining  it  as  a  result  of  gravitation 
have  rendered  it  one  of  the  most  interesting  of  the 
moon's  numerous  irregularities  (cf.  chapter  XL,  §  240,  and 
chapter  XIIL,  §  287). 

202.  Halley  also   rendered   good   service   to   astronomy 
by  calling   attention   to   the   importance   of  the   expected 
transits  of  Venus  across  the  sun  in  1761   and  1769  as  a 
means   of    ascertaining    the    distance    of    the    sun.      The 
method  had  been  suggested  rather  vaguely  by  Kepler,  and 
more  definitely  by  James  Gregory  in  his  Optics  published 
in    1663.      The    idea   was   first   suggested    to   Halley   by 


$$  aoi—204]  Halky  255 

his  observation  of  the  transit  of  Mercury  in  1677.  In 
three  papers  published  by  the  Royal  Society  he  spoke 
warmly  of  the  advantages  of  the  method,  and  discussed 
in  some  detail  the  places  and  means  most  suitable  for 
observing  the  transit  of  1761.  He  pointed  out  that  the 
desired  result  could  be  deduced  from  a  comparison  of 
the  durations  of  the  transit  of  Venus,  as  seen  from  different 
stations  on  the  earth,  i.e.  of  the  intervals  between  the  first 
appearance  of  Venus  on  the  sun's  disc  and  the  final  dis- 
appearance, as  seen  at  two  or  more  different  stations.  He 
estimated,  moreover,  that  this  interval  of  time,  which  would 
be  several  hours  in  length,  could  be  measured  with  an 
error  of  only  about  two  seconds,  and  that  in  consequence 
the  method  might  be  relied  upon  to  give  the  distance  of 
the  sun  to  within  about  ^-^  part  of  its  true  value.  As  the 
current  estimates  of  the  sun's  distance  differed  among  one 
another  by  20  or  30  per  cent,  the  new  method,  expounded 
with  Halley's  customary  lucidity  and  enthusiasm,  not  un- 
naturally stimulated  astronomers  to  take  great  trouble  to 
carry  out  Halley's  recommendations.  The  results,  as  we 
shall  see  (§  227),  were,  however,  by  no  means  equal  to 
Halley's  expectations. 

203.  In   1718  Halley  called   attention  to  the  fact   thaf 
three  well-known  stars,  Sirius,  Procyon,  and  Arcturus,  had 
changed   their  angular  distances   from   the   ecliptic   since 
Greek  times,  and  that  Sirius  had  even  changed  its  position 
perceptibly  since  the   time   of  Tycho    Brahe.      Moreover 
comparison  of  the  places  of  other  stars  shewed  that  the 
changes  could  not  satisfactorily  be  attributed  to  any  motion 
of  the   ecliptic,  and  although  he  was  well  aware  that  the 
possible  errors  of  observation  were  such  as   to  introduce 
a  considerable  uncertainty  into  the  amounts  involved,  he 
felt   sure   that   such   errors   could   not  wholly  account   for 
the  discrepancies   noticed,  but   that   the  stars  in  question 
must  have  really  shifted  their  positions  in  relation   to  the 
rest ;   and  he  naturally  inferred   that  it  would  be  possible 
to  detect  similar  proper  motions  (as  they  are  now  called)  in 
other  so-called  "  fixed  "  stars. 

204.  He  also  devoted  a  good  deal  of  time  to  the  stand- 
ing astronomical  problem   of  improving  the  tables  of  the 
moon  and   planets,   particularly   the    former.      He   made 


256  A  Short  History  of  Astronomy  [CH.  x. 

observations  of  the  moon  as  early  as  1683,  and  by  means 
of  them  effected  some  improvement  in  the  tables.  In 
1676  he  had  already  noted  defects  in  the  existing  tables 
of  Jupiter  and  Saturn,  and  ultimately  satisfied  himself  of 
the  existence  of  certain  irregularities  in  the  motion  of  these 
two  planets,  suspected  long  ago  by  Horrocks  (chapter  vin., 
§  156);  these  irregularities  he  attributed  correctly  to  the 
perturbations  of  the  two  planets  by  one  another,  though 
he  was  not  mathematician  enough  to  work  out  the  theory ; 
from  observation,  however,  he  was  able  to  estimate  the 
irregularities  in  question  with  fair  accuracy  and  to  improve 
the  planetary  tables  by  making  allowance  for  them.  But 
neither  the  lunar  nor  the  planetary  tables  were  ever  com- 
pleted in  a  form  which  Halley  thought  satisfactory.  By 
1719  they  were  printed,  but  kept  back  from  publication, 
in  hopes  that  subsequent  improvements  might  be  effected. 
After  his  appointment  as  Astronomer  Royal  in  succession 
to  Flamsteed  (1720)  he  devoted  special  attention  to  getting 
fresh  observations  for  this  purpose,  but  he  found  the 
Observatory  almost  bare  of  instruments,  those  used  by 
Flamsteed  having  been  his  private  property,  and  having 
been  removed  as  such  by  his  heirs  or  creditors.  Although 
Halley  procured  some  instruments,  and  made  with  them 
a  number  of  observations,  chiefly  of  the  moon,  the  age  (63) 
at  which  he  entered  upon  his  office  prevented  him  from 
initiating  much,  or  from  carrying  out  his  duties  with  great 
energy,  and  the  observations  taken  were  in  consequence 
only  of  secondary  importance,  while  the  tables  for  the 
.improvement  of  which  they  were  specially  designed  were 
only  finally  published  in  1752,  ten  years  after  the  death 
of  their  author.  Although  they  thus  appeared  many  years 
after  the  time  at  which  they  were  virtually  prepared  and 
owed  little  to  the  progress  of  science  during  the  interval, 
they  at  once  became  and  for  some  time  remained  the 
standard  tables  for  both  the  lunar  and  planetary  motions 
(cf.  §  226,  and  chapter  XL,  §  247). 

205.  Halley 's  remarkable  versatility  in  scientific  work  is 
further  illustrated  by  the  labour  which  he  expended  in 
editing  the  writings  of  the  great  Greek  geometer  Apollonius 
(chapter  u.,  §  38)  and  the  star  catalogue  of  Ptolemy 
(chapter  n.,  §  50).  He  was  also  one  of  the  first  of  modern 


$$  2o5,  206]  Halley  257 

astronomers  to  pay  careful  attention  to  the  effects  to  be 
observed  during  a  total  eclipse  of  the  sun,  and  in  the 
vivid  description  which  he  wrote  of  the  eclipse  of  1715, 
besides  referring  to  the  mysterious  corona,  which  Kepler 
and  others  had  noticed  before  (chapter  vii.,  §  145),  he 
called  attention  also  to  "  a  very  narrow  streak  of  a  dusky 
but  strong  Red  Light,"  which  was  evidently  a  portion  of 
that  remarkable  envelope  of  the  sun  which  has  been  so 
extensively  studied  in  modern  times  (chapter  xm.,  §  301) 
under  the  name  of  the  chromosphere. 

It  is  worth  while  to  notice,  as  an  illustration  of  Halley's 
unselfish  enthusiasm  for  science  and  of  his  power  of  looking 
to  the  future,  that  two  of  his  most  important  pieces  of  work, 
by  which  certainly  he  is  now  best  known,  necessarily 
appeared  during  his  lifetime  as  of  little  value,  and  only 
bore  their  fruit  after  his  death  (1742),  for  his  comet  only 
returned  in  1759,  when  he  had  been  dead  17  years,  and 
the  first  of  the  pair  of  transits  of  Venus,  from  which  he 
had  shewn  how  to  deduce  the  distance  of  the  sun,  took 
place  two  years  later  still  (§  227). 

206.  The  third  Astronomer  Royal,  James  Bradley,  is 
popularly  known  as  the  author  of  two  memorable  dis- 
coveries, viz.  the  aberration  of  light  and  the  nutation 
of  the  earth's  axis.  Remarkable  as  these  are  both  in 
themselves  and  on  account  of  the  ingenious  and  subtle 
reasoning  and  minutely  accurate  observations  by  means  of 
which  they  were  made,  they  were  in  fact  incidents  in  a  long 
and  active  astronomical  career,  which  resulted  in  the 
execution  of  a  vast  mass  of  work  of  great  value. 

The  external  events  of  Bradley's  life  may  be  dealt  with 
very  briefly.  Born  in  1693,  he  proceeded  in  due  course 
to  Oxford  (B.A.  1714,  M.A.  1717),  but  acquired  his  first 
knowledge  of  astronomy  and  his  marked  taste  for  the 
subject  from  his  uncle  James  Pound,  for  many  years  rector 
of  Wansted  in  Essex,  who  was  one  of  the  best  observers  of 
the  time.  Bradley  lived  with  his  uncle  for  some  years  after 
leaving  Oxford,  and  carried  out  a  number  of  observations 
in  concert  with  him.  The  first  recorded  observation  of 
Bradley's  is  dated  1715,  and  by  1718  he  was  sufficiently 
well  thought  of  in  the  scientific  world  to  receive  the  honour 
of  election  as  a  Fellow  of  the  Royal  Society.  But,  as  his 

17 


258  A  Short  History  of  Astronomy  [€H.  X. 

biographer  *  remarks,  "  it  could  not  be  foreseen  that  his 
astronomical  labours  would  lead  to  any  establishment  in 
life,  and  it  became  necessary  for  him  to  embrace  a  pro- 
fession." He  accordingly  took  orders,  and  was  fortunate 
enough  to  be  presented  almost  at  once  to  two  livings,  the 
duties  attached  to  which  do  not  seem  to  have  interfered 
appreciably  with  the  prosecution  of  his  astronomical  studies 
at  Wansted. 

In  1721  he  was  appointed  Savilian  Professor  of  Astro- 
nomy at  Oxford,  and  resigned  his  livings.  The  work  of  the 
professorship  appears  to  have  been  very  light,  and  for  more 
than  ten  years  he  continued  to  reside  chiefly  at  Wansted, 
even  after  his  uncle's  death  in  1724.  In  1732  he  took  a 
house  in  Oxford  and  set  up  there  most  of  his  instruments, 
leaving,  however,  at  Wansted  the  most  important  of  all, 
the  "  zenith-sector,"  with  which  his  two  famous  discoveries 
were  made.  Ten  years  afterwards  Halley's  death  rendered 
the  post  of  Astronomer  Royal  vacant,  and  Bradley  received 
the  appointment. 

The  work  of  the  Observatory  had  been  a  good  deal 
neglected  by  Halley  during  the  last  few  years  of  his  life, 
and  Bradley's  first  care  was  to  effect  necessary  repairs  in 
the  instruments.  Although  the  equipment  of  the  Obser- 
vatory with  instruments  worthy  of  its  position  and  of  the 
state  of  science  at  the  time  was  a  work  of  years,  Bradley 
had  some  of  the  most  important  instruments  in  good 
working  order  within  a  few  months  of  his  appointment, 
and  observations  were  henceforward  made  systematically. 
Although  the  20  remaining  years  of  his  life  (1742-1762) 
were  chiefly  spent  at  Greenwich  in  the  discharge  of  the 
duties  of  his  office  and  in  researches  connected  with  them, 
he  retained  his  professorship  at  Oxford,  and  continued  to 
make  observations  at  Wansted  at  least  up  till  1747. 

207.  The  discovery  of  aberration  resulted  from  an  attempt 
to  detect  the  parallactic  displacement  of  stars  which  should 
result  from  the  annual  motion  of  the  earth.  Ever  since 
the  Coppernican  controversy  had  called  attention  to  the 
importance  of  the  problem  (cf.  chapter  iv.,  §  92,  and 
chapter  vi.,  §  129),  it  had  naturally  exerted  a  fascination 

*  Rigaud,  in  the  memoirs  prefixed  to  Bradley's  Miscellaneous 
Works. 


[To  face  p.  258. 


$207]  Bradley:    Aberration  259 

on  the  minds  of  observing  astronomers,  many  of  whom  had 
tried  to  detect  the  motion  in  question,  and  some  of  whom 
(including  the  "  universal  claimant "  Hooke)  professed  to 
have  succeeded.  Actually,  however,  all  previous  attempts 
had  been  failures,  and  Bradley  was  no  more  successful  than 
his  predecessors  in  this  particular  undertaking,  but  was 
able  to  deduce  from  his  observations  two  results  of  great 
interest  and  of  an  entirely  unexpected  character. 

The  problem  which  Bradley  set  himself  was  to  examine 
whether  any  star  could  be  seen  to  have  in  the  course  of  the 
year  a  slight  motion  relative  to  others  or  relative  to  fixed 
points  on  the  celestial  sphere  such  as  the  pole.  It  was 
known  that  such  a  motion,  if  it  existed,  must  be  very 
small,  and  it  was  therefore  evident  that  extreme  delicacy 
in  instrumental  adjustments  and  the  greatest  care  in  obser- 
vation would  have  to  be  employed.  Bradley  worked  at  first 
in  conjunction  with  his  friend  ,SVz ;#*/£/ Mo/yneux(i6Sg~ij2S)^ 
who  had  erected  a  telescope  at  Kew.  In  accordance  with  the 
method  adopted  in  a  similar  investigation  by  Hooke,  whose 
results  it  was  desired  to  test,  the  telescope  was  fixed  in  a 
nearly  vertical  position,  so  chosen  that  a  particular  star  in 
the  Dragon  (y  Draconis)  would  be  visible  through  it  when 
it  crossed  the  meridian,  and  the  telescope  was  mounted 
with  great  care  so  as  to  maintain  an  invariable  position 
throughout  the  year.  If  then  the  star  in  question  were  to 
undergo  any  motion  which  altered  its  distance  from  the 
pole,  there  would  be  a  corresponding  alteration  in  the  posi- 
tion in  which  it  would  be  seen  in  the  field  of  view  of 
the  telescope.  The  first  observations  were  taken  on 
December  i4th,  1725  (N.S.),  and  by  December  28th 
Bradley  believed  that  he  had  already  noticed  a  slight  dis- 
placement of  the  star  towards  the  south.  This  motion 
was  clearly  verified  on  January  ist,  and  was  then  observed 
to  continue  ;  in  the  following  March  the  star  reached  its 
extreme  southern  position,  and  then  began  to  move  north- 
wards again.  In  September  it  once  more  altered  its 
direction  of  motion,  and  by  the  end  of  the  year  had 
completed  the  cycle  of  its  changes  and  returned  to  its 
original  position,  the  greatest  change  in  position  amounting 
to  nearly  40' . 

The  star  was  thus  observed  to  go  through  some  annual 


260  A  Short  History  of  Astronomy  [Cn.  X. 

motion.  It  was,  however,  at  once  evident  to  Bradley  that 
this  motion  was  not  the  parallactic  motion  of  which  he 
was  in  search,  for  the  position  of  the  star  was  such  that 
parallax  would  have  made  it  appear  farthest  south  in 
December  and  farthest  north  in  June,  or  in  each  case  three 
months  earlier  than  was  the  case  in  the  actual  observations. 
Another  explanation  which  suggested  itself  was  that  the 
earth's  axis  might  have  a  to-and-fro  oscillatory  motion  or 
nutation  which  would  alter  the  position  of  the  celestial  pole 
and  hence  produce  a  corresponding  alteration  in  the  position 
of  the  star.  Such  a  motion  of  the  celestial  pole  would 
evidently  produce  opposite  effects  on  two  stars  situated  on 
opposite  sides  of  it,  as  any  motion  which  brought  the  pole 
nearer  to  one  star  of  such  a  pair  would  necessarily  move 
it  away  from  the  other.  Within  a  fortnight  of  the  decisive 
observation  made  on  January  ist  a  star*  had  already  been 
selected  for  the  application  of  this  test,  with  the  result  which 
can  best  be  given  in  Bradley's  own  words : — 

"  A  nutation  of  the  earth's  axis  was  one  of  the  firsv  things  that 
offered  itself  upon  this  occasion,  but  it  was  soon  found  to  be 
insufficient;  for  though  it  might  have  accounted  for  the  change 
of  declination  in  y  Draconis,  yet  it  would  not  at  the  same  time 
agree  with  the  phaenomenain  other  stars  ;  particularly  in  a  small 
one  almost  opposite  in  right  ascension  to  y  Draconis,  at  about 
the  same  distance  from  the  north  pole  of  the  equator  :  for  though 
this  star  seemed  to  move  the  same  way  as  a  nutation  of  the 
earth's  axis  would  have  made  it,  yet,  it  changing  its  declination 
but  about  half  as  much  as  y  Draconis  in  the  same  time,  (as 
appeared  upon  comparing  the  observations  of  both  made  upon 
the  same  days,  at  different  seasons  of  the  year,)  this  plainly 
proved  that  the  apparent  motion  of  the  stars  was  not  occasioned 
by  a  real  nutation,  since,  if  that  had  been  the  cause,  the  altera- 
tion in  both  stars  would  have  been  near  equal." 

One  or  two  other  explanations  were  tested  and  found 
insufficient,  and  as  the  result  of  a  series  of  observations 
extending  over  about  two  years,  the  phenomenon  in  ques- 
tion, although  amply  established,  still  remained  quite 
unexplained. 

By  this  time  Bradley  had  mounted  an  instrument  of  his 

*  A  telescopic  star  named  37  Camelopardi  in  Flamsteed's 
catalogue. 


$  2c8]  Aberration  261 

own  at  Wansted,  so  arranged  that  it  was  possible  to  observe 
through  it  the  motions  of  stars  other  tfcan  y  Draconis. 

Several  stars  were  watched  carefully  throughout  a  year, 
and  the  observations  thus  obtained  gave  Bradley  a  fairly 
complete  knowledge  of  the  geometrical  laws  according  to 
which  the  motions  varied  both  from  star  to  star  and  in 
the  course  of  the  year. 

208.  The  true  explanation  of  aberration,  as  the  pheno- 
menon in  question  was  afterwards  called,  appears  to  have 
occurred  to  him  about  September,  1728,  and  was  published 
to  the  Royal  Society,  after  some  further  verification,  early 
in  the  following  year.  According  to  a  well-known  story,* 
he  noticed,  while  sailing  on  the  Thames,  that  a  vane  on 
the  masthead  appeared  to  change  its  direction  every  time 
that  the  boat  altered  its  course,  and  was  informed  by  the 
sailors  that  this  change  was  not  due  to  any  alteration  in 
the  wind's  direction,  but  to  that  of  the  boat's  course.  In 
fact  the  apparent  direction  of  the  wind,  as  shewn  by  the 
vane,  was  not  the  true  direction  of  the  wind,  but  resulted 
from  a  combination  of  the  motions  of  the  wind  and  of  the 
boat,  being  more  precisely  that  of  the  motion  of  the  wind 
relative  to  the  boat.  Replacing  in  imagination  the  wind 
by  light  coming  from  a  star,  and  the  boat  shifting  its 
course  by  the  earth  moving  round  the  sun  and  continually 
changing  its  direction  of  motion,  Bradley  arrived  at  an 
explanation  which,  when  worked  out  in  detail,  was  found 
to  account  most  satisfactorily  for  the  apparent  changes  in 
the  direction  of  a  star  which  he  had  been  studying.  His 
own  account  of  the  matter  is  as  follows  : — 

"  At  last  I  conjectured  that  all  the  phaenomena  hitherto  men- 
tioned proceeded  from  the  progressive  motion  of  light  and  the 
earth's  annual  motion  in  its  orbit.  For  I  perceived  that,  if  light 
was  propagated  in  time,  the  apparent  place  of  a  fixed  object 
would  not  be  the  same  when  the  eye  is  at  rest,  as  when  it  is 
moving  in  any  other  direction  than  that  of  the  line  passing 
through  the  eye  and  object ;  and  that  when  the  eye  is  moving 

*  The  story  is  given  in  T.  Thomson's  History  of  the  Royal  Society, 
published  more  than  80  years  afterwards  (1812),  but  I  have  not  been 
able  to  find  any  earlier  authority  for  it.  Bradley's  own  account  of 
his  ducovcry  gives  a  number  of  details,  but  has  wo  allusion  to  this 


262 


A  Short  History  of  Astronomy 


[Cn.  X. 


in  different  directions,  the  apparent  place  of  the  object  would  be 
different. 

"  I  considered  this  matter  in  the  following  manner.  I  imagined 
c  A  to  be  a  ray  of  light,  falling  perpendicularly  upon  the  line 
B  D  ;  then  if  the  eye  is  at  rest  at  A,  the  object  must  appear  in 
the  direction  A  c,  whether  light  be  propagated  in  time  or  in  an 
instant.  But  if  the  eye  is  moving  from  B  towards  A,  and  light 
is  propagated  in  time,  with  a  velocity  that  is  to  the  velocity  uf 
the  eye,  as  c  A  to  B  A  ;  then  light  moving  from  c  to  A,  whilst 
the  eye  moves  from  B  to  A,  that  particle  of  it  by  which  the  object 
will  be  discerned  when  the  eye  in  its 
motion  comes  to  A,  is  at  c  when  the  eye 
is  at  B.  Joining  the  points  B,  c,  I  sup- 
posed the  line  c  B  to  be  a  tube  (inclined 
to  the  line  B  D  in  the  angle  D  B  c)  of  such 
a  diameter  as  to  admit  of  but  one  particle 
of  light ;  then  it  was  easy  to  conceive  that 
the  particle  of  light  at  c  (by  which  the 
object  must  be  seen  when  the  eye,  as  it 
moves  along,  arrives  at  A)  would  pass 
through  the  tube  B  c,  if  it  is  inclined  to 
B  D  in  the  angle  D  B  c,  and  accompanies 
the  eye  in  its  motion  from  B  to  A  ;  and 
that  it  could  not  come  to  the  eye,  placed 
behind  such  a  tube,  if  it  had  any  other 
inclination  to  the  line  B  D.  .  .  . 

"  Although  therefore  the  true  or  real 
place  of  an  object  is  perpendicular  to  the 
line  in  which  the  eye  is  moving,  yet  the 
visible  place  will  not  be  so,  since  that, 
no  doubt,  must  be  in  the  direction  of  the 
tube  ;  but  the  difference  between  the  true 
and  apparent  place  will  be  (caeteris  pari- 


D  A  B 

FIG.  74. — The  aberra- 


the  Phil.  Trans. 


tion  of  light.  From  bus)  greater  or  less,  according  to  the 
Bradley's  paper  in  different  proportion  between  the  velocity 
of  light  and  that  of  the  eye.  So  that  if 
we  could  suppose  that  li^ht  was  propa- 
gated in  an  instant,  then  there  would  be  no.  difference  between 
the  real  and  visible  place  of  an  object,  although  the  eye  were 
in  motion  ;  for  in  that  case,  A  c  being  infinite  with  respect 
to  A  B,  the  angle  A  c  B  (the  difference  between  the  true  and 
visible  place)  vanishes.  But  if  light  be  propagated  in  time, 
(which  I  presume  will  readily  be  allowed  by  most  of  the 
philosophers  of  this  age,)  then  it  is  evident  from  the  foregoing 
considerations,  that  there  will  be  always  a  difference  between 
the  real  and  visible  place  of  an  object,  unless  the  eye  is  moving 
either  directly  towards  or  from  the  object." 


20Q] 


Aberration 


263 


Bradley's  explanation  shews  that  the  apparent  position  of 
a  star  is  determined  by  the  motion  of  the  star's  light  relative 
to  the  earth,  so  that  the  star  appears  slightly  nearer  to  the 
point  on  the  celestial  sphere  towards  which  the  earth  is 
moving  'than  would  otherwise  be  the  case.  A  familiar 
illustration  of  a  precisely  analogous  effect  may  perhaps  be 
of  service.  Any  one  walking  on  a  rainy  but  windless  day 
protects  himself  most  effectually  by  holding  his  umbrella, 
not  immediately  over  his  head,  but  a  little  in  front,  exactly 
as  he  would  do  if  he  were  at  rest  and  there  were  a  slight 
wind  blowing  in  his  face.  In  fact,  if  he  were  to  ignore 
his  own  motion  and  pay  attention  only  to  the  direction  in 
which  he  found  it  advisable  to  point  his  umbrella,  he  would 
believe  that  there  was  a  slight  head-wind  blowing  the  rain 
towards  hiir. 

209.  The  passage  quoted  from  Bradley's  paper  deals 
only  with  the  simple  case  in  which  the  star  is  at  right  angles 
to  the  direction  of  the  earth's  motion.  He  - 
shews  elsewhere  that  if  the  star  is  in  any  \ 
other  direction  the  effect  is  of  the  same  kind 
but  less  in  amount.  In  Bradley's  figure 
(fig.  74)  the  amount  of  the  star's  displace- 
ment from  its  true  pqsition  is  represented  by 
the  angle  B  c  A,  which  depends  on  the  pro- 
portion between  the  lines  A  c  and  A  B  ;  but 
if  (as  in  fig.  75)  the  earth  is  moving  (without 
change  of  speed)  in  the  direction  A  B'  instead 
of  A  B,  so  that  the  direction  of  the  star  is 
oblique  to  it,  it  is  evident  from  the  figure 
that  the  star's  displacement,  represented  by 
the  angle  A  c  B',  is  less  than  before  ;  and 
the  amount  varies  according  to  a  simple 
mathematical  law*  with  the  angle  between 
the  two  directions.  It  follows  therefore 
that  the  displacement  in  question  is  different 
for  different  stars,  as  Bradley's  observations 
had  already  shewn,  and  is,  moreover,  dif- 
ferent for  the  same  star  in  the  course  of  the 
year,  so  that  a  star  appears  to  describe  a 
curve  which  is  very  nearly  an  ellipse  (fig.  76),  the  centre  (s) 
*  It  is  k  sin  CAB,  where  k  is  the  constant  of  aberration. 


264 


A  Short  History  of  Astronomy 


[CH.   X. 


FIG.  76. — The  aberrational  ellipse. 


corresponding  to  the  position  which  the  star  would  occupy 
if  aberration  did  not  exist.  It  is  not  difficult  to  see  that, 
wherever  a  star  is  situated,  the  earth's  motion  is  twice  a 
year,  at  intervals  of  six  months,  at  right  angles  to  the  direc- 
tion of  the  star,  and  that  at  these  times  the  star  receives  the 
greatest  possible  displacement  from  its  mean  position,  and 
is  consequently  at  the  ends  of  the  greatest  axis  of  the 
ellipse  which  it  describes,  as  at  A  and  A',  whereas  at  inter- 
mediate times  it 
undergoes  its  least 
displacement,  as  at 
B  and  B'.  The 
greatest  displace- 
ment  s  A,  or  half  of 
A  A',  which  is  the 
same  for  all  stars, 
is  known  as  the  con- 
stant of  aberration, 
and  was  fixed  by 
Bradley  at  between 
20"  and  2o|",  the 
value  at  present  accepted  being  2o"'47.  The  least  displace- 
ment, on  the  other  hand,  s  B,  or  half  of  B  B',  was  shewn 
to  depend  in  a  simple  way  upon  the  star's  distance  from 
the  ecliptic,  being  greatest  for  stars  farthest  from  the 
ecliptic. 

210.  The  constant  of  aberration,  which  is  represented  by 
the  angle  A  c  B  in  fig.  74,  depends  only  on  the  ratio  between 
A  c  and  A  B,  which  are  in  turn  proportional  to  the  velocities 
of  light  and  of  the  earth.  Observations  of  aberration  give 
then  the  ratio  of  these  two  velocities.  From  Bradley's 
value  of  the  constant  of  aberration  it  follows  by  an  easy 
calculation  that  the  velocity  of  light  is  about  10,000  times 
that  of  the  earth  ;  Bradley  also  put  this  result  into  the  form 
that  light  travels  from  the  sun  to  the  earth  in  8  minutes  13 
seconds.  From  observations  of  the  eclipses  of  Jupiter's 
moons,  Roemer  and  others  had  estimated  the  same  interval 
at  from  8  to  n  minutes  (chapter  VIIL,  §  162);  and  Bradley 
was  thus  able  to  get  a  satisfactory  confirmation  of  the  truth 
of  his  discovery.  Aberration  being  once  established,  the 
same  calculation  could  be  used  to  give  the  most  accurate 


M  210—213]  Aberration  «  265 

measure  of  the  velocity  of  light  in  terms  of  the  dimensions 
of  the  earth's  orbit,  the  determination  of  aberration  being 
susceptible  of  considerably  greater  accuracy  than  the 
corresponding  measurements  required  for  Roemer's  method. 

211.  One  difficulty  in  the  theory  of  aberration  deserves 
mention.     Bradley's  own  explanation,  quoted  above,  refers 
to  light  as  a  material  substance  shot  out  from  the  star  or 
other   luminous   body.     This  was  in  accordance  with  the 
corpuscular   theory   of  light,  which  was  supported  by  the 
great   weight   of   Newton's   authority   and    was   commonly 
accepted  in  the  i8th  century.     Modern  physicists,  however, 
have  entirely  abandoned  the  corpuscular  theory,  and  regard 
light    as    a   particular  form    of   wave-motion    transmitted 
through   ether.      From   this   point   of  view   Bradley's   ex- 
planation  and  the  physical  illustrations  given  are  far  less 
convincing;  the  question  becomes  in  fact  one  of  considerable 
difficulty,  and  the  most  careful  and  elaborate  of  modern 
investigations  cannot  be  said  to  be  altogether  satisfactory. 
The  curious   inference   may  be   drawn  that,   if  the  more 
correct  modern  notions  of  the  nature  of  light  had  prevailed 
in    Bradley's   time,   it   must   have  been  very  much    more 
difficult,  if  not  impracticable,  for  him  to  have'  thought  of  his 
explanation  of  the  stellar  motions  which  he  was  studying ; 
and  thus  an   erroneous   theory  led   to  a   most   important 
discovery. 

212.  Bradley  had  of  course   not  forgotten  the  original 
object  of  his  investigation.     He  satisfied  himself,  however, 
that  the  agreement  between  the  observed  positions  of  7  Dra- 
conis  and  those  which   resulted   from   aberration   was   so 
close  that  any  displacement  of  a  star  due  to  parallax  which 
might  exist  must  certainly  be  less  than  2",  and  probably 
not  more  than  |",  so  that  the  large  parallax  amounting  to 
nearly  30",  which  Hooke  claimed  to  have  detected,  must 
certainly  be  rejected  as  erroneous. 

From  the  point  of  view  of  the  Coppernican  controversy, 
however,  Bradley's  discovery  was  almost  as  good  as  the 
discovery  of  a  parallax  ;  since  if  the  earth  were  at  rest 
no  explanation  of  the  least  plausibility  could  be  given  of 
aberration. 

213.  The  close  agreement  thus  obtained  between  theory 
and  observation  would  have  satisfied  an   astronomer  less 


'266  ^4  Short  His  lory  of  Astronomy  [CH.  x. 

accurate  and  careful  than  Bradley.     But  in   his  paper  on 
aberration  (1729)  we  find  him  writing  : — 

"  I  have  likewise  met  with  some  small  varieties  in  the  declina- 
tion of  other  stars  in  different  years  which  do  not  seem  to 
proceed  from  the  same  cause.  .  .  .  But  whether  these  small 
alterations  proceed  from  a  regular  cause,  or  are  occasioned  by 
any  change  in  the  materials,  etc.,  of  my  instrument,  I  am  not  yet 
able  fully  to  determine." 

The  slender  clue  thus  obtained  was  carefully  followed 
up  and  led  to 'a  second  striking  discovery,  which  affords 
one  of  the  most  beautiful  illustrations  of  the  important 
results  which  can  be  deduced  from  the  study  of  "  residual 
phenomena."  Aberration  causes  a  star  to  go  through  a 
cyclical  series  of  changes  in  the  course  of  a  year  ;  if  there- 
fore at  the  end  of  a  year  a  star  is  found  not  to  have 
returned  to  its  original  place,  some  other  explanation  of 
the  motion  has  to  be  sought.  Precession  was  one  known 
cause  of  such  an  alteration ;  but  Bradley  found,  at  the  end 
of  his  first  year's  set  of  observations  at  Wansted,  that  the 
alterations  in  the  positions  of  various  stars  differed  by  a 
minute  amount  (not  exceeding  2")  from  those  which  would 
have  resulted  from  the  usual  estimate  of  precession ;  and 
that,  although  an  alteration  in  the  value  of  precession  would 
account  for  the  observed  motions  of  some  of  these  stars, 
it  would  have  increased  the  discrepancy  in  the  case  of 
others.  A  nutation  or  nodding  of  the  earth's  axis  had, 
as  we  have  seen  (§  207),  already  presented  itself  to  him 
as  a  possibility ;  and  although  it  had  been  shewn  to  be 
incapable  of  accounting  for  the  main  phenomenon — due  to 
aberration — it  might  prove  to  be  a  satisfactory  explanation 
of  the  much  smaller  residual  motions.  It  soon  occurred 
to  Bradley  that  such  a  nutation  might  be  due  to  the  action 
of  the  moon,  as  both  observation  and  the  Newtonian 
explanation  of  precession  indicated  : — 

"  I  suspected  that  the  moon's  action  upon  the  equatorial  parts 
of  the  earth  might  produce  these  effects  :  for  if  the  precession 
of  the  equinox  be,  according  to  Sir  Isaac  Newton's  principles, 
caused  by  the  actions  of  the  sun  and  moon  upon  those  parts, 
the  plane  of  the  moon's  orbit  being  at_  one  time  above  ten 
degrees  more  inclined  to  the  plane  of  the  equator  than  at 
another,  it  was  reasonable  to  conclude,  that  the  part  of  the 


$  2i3]  Nutation  267 

whole  annual  precession,  which  arises  from  her  action,  would 
in  different  years  be  varied  in  its  quantity  ;  whereas  the  plane 
of  the  ecliptic,  wherein  the  sun  appears,  keeping  always  nearly 
the  same  inclination  to  the  equator,  that  part  of  the  precession 
which  is  owing  to  the  sun's  action  may  be  the  same  every  year ; 
and  from  hence  it  would  follow,  that  although  the  mean  annual 
precession,  proceeding  from  the  joint  actions  of  the  sun  and 
moon,  were  50",  yet  the  apparent  annual  precession  might 
sometimes  exceed  an<l  sometimes  fall  short  of  that  mean 
qmntity,  according  to  the  various  situations  of  the  nodes  of 
the  moon's  orbit." 

Newton  in  his  discussion  of  precession  (chapter  ix.,  §  188; 
Principia,  Book  III.,  proposition  21)  had  pointed  out 
the  existence  of  a  small  irregularity  with  a  period  of  six 
months.  But  it  is  evident,  on  looking  at  this  discussion 
of  the  effect  of  the  solar  and  lunar  attractions  on  the 
protuberant  parts  of  the  earth,  that  the  various  alterations 
in  the  positions  of  the  sun  and  moon  relative  to  the  earth 
might  be  expected  to  produce  irregularities,  and  that  the 
uniform  precessional  motion  known  from  observation  and 
deduced  from  gravitation  by  Newton  was,  as  it  were,  only 
a  smoothing  out  of  a  motion  of  a  much  more  complicated 
character.  Except  for  the  allusion  referred  to,  Newton 
made  no  attempt  to  discuss  these  irregularities,  and  none 
of  them  had  as  yet  been  detected  by  observation. 

Of  the  numerous  irregularities  of  this  class  which  are  now 
known,  and  which  may  be  referred  to  generally  as  nutation, 
that  indicated  by  Bradley  in  the  passage  just  quote!  is 
by  far  the  most  important.  As  soon  as  the  idea  ot  an 
irregularity  depending  on  the  position  of  the  moon's  nodes 
occurred  to  him,  he  saw  that  it  would  be  desirable  to  watch 
the  motions  of  several  stars  during  the  whole  period  (about 
19  years)  occupied  by  the  moon's  nodes  in  performing  the 
circuit  of  the  ecliptic  and  returning  to  the  same  position. 
This  inquiry  was  successfully  carried  out  between  1727  and 
1747  with  the  telescope  mounted  at  Wansted.  When  the 
moon's  nodes  had  performed  half  their  revolution,  i.e. 
after  about  nine  years,  the  correspondence  between  the 
displacements  of  the  stars  and  the  changes  in  the  moon's 
orbit  was  so  close  that  Bradley  was  satisfied  with  the  general 
correctness  of  his  theory,  and  in  1737  he  communicated  the 
result  privately  to  Maupertuis  (§  221),  with  whom  he  had 


268 


A  Short  History  of  Astronomy 


[C'H.   X. 


had  some  scientific  correspondence.  Maupertuis  appears 
to  have  told  others,  but  Bradley  himself  waited  patiently 
for  the  completion  of  the  period  which  he  regarded  as 
necessary  for  the  satisfactory  verification  of  his  theory,  and 
only  published  his  results  definitely  at  the  beginning  of 
1748. 

214.  Bradley's  observations  established  the  existence  of 
certain  alterations  in  the  positions  of  various  stars,   which 


FIG,  77. — Precession  and  nutation. 

could  be  accounted  for  by  supposing  that,  on  the  one 
hand,  the  distance  of  the  pole  from  the  ecliptic  fluctu- 
ated, and  that,  on  the  other,  the  precessional  motion  of 
the  pole  was  not  uniform,  but  varied  slightly  in  speed. 
John  Machin  (?  -1751),  one  of  the  best  English  mathe- 
maticians of  the  time,  pointed  out  that  these  effects  would 
be  produced  if  the  pole  were  supposed  to  describe  on  the 
celestial  sphere  a  minute  circle  in  a  period  of  rather  less 


$$  2i4—2i6]  Nutation  269 

than  19  years— being  that  of  the  revolution  of  the  nodes 
of  the  moon's  orbit — round  the  position  which  it  would 
occupy  if  there  were  no  nutation,  but  a  uniform  precession. 
Bradley  found  that  this  hypothesis  fitted  his  observations, 
but  that  it  would  be  better  to  replace  the  circle  by  a 
slightly  flattened  ellipse,  the  greatest  and  least  axes  of  which 
he  estimated  at  about  18"  and  16"  respectively.*  This 
ellipse  would  be  about  as  large  as  a  shilling  placed  in  a 
slightly  oblique  position  at  a  distance  of  300  yards  from 
the  eye.  The  motion  of  the  pole  was  thus  shewn  to  be 
a  double  one ;  as  the  result  of  precession  and  nutation 
combined  it  describes  round  the  pole  of  the  ecliptic  "a 
gently  undulated  ring,"  as  represented  in  the  figure,  in 
which,  however,  the  undulations  due  to  nutation  are 
enormously  exaggerated. 

215.  Although   Bradley  was  aware   that   nutation   must 
be   produced   by   the   action    of    the   moon,   he   left    the 
theoretical    investigation     of    its    cause    to    more    skilled 
mathematicians  than  himself. 

In  the  following  year  (1749)  the  French  mathematician 
D'Alembert  (chapter  XL,  §  232)  published  a  treatise  t  in 
which  not  only  precession,  but  also  a  motion  of  nutation 
agreeing  closely  with  that  observed  by  Bradley,  were  shewn 
by  a  rigorous  process  of  analysis  to  be  due  to  the  attraction 
of  the  moon  on  the  protuberant  parts  of  the  earth  round 
the  equator  (cf.  chapter  ix.,  §  187),  while  Newton's  ex- 
planation of  precession  was  confirmed  by  the  same  piece 
of  work.  Euler  (chapter  XL,  §  236)  published  soon  after- 
wards another  investigation  of  the  same  subject;  and  it 
has  been  studied  afresh  by  many  mathematical  astronomers 
since  that  time,  with  the  result  that  Bradley's  nutation 
is  found  to  be  only  the  most  important  of  a  long  series 
of  minute  irregularities  in  the  motion  of  the  earth's  axis. 

216.  Although  aberration  and  nutation  have   been  dis- 
cussed  first,   as   being    the   most   important   of   Bradley's 

*  His  observations  as  a  matter  of  fact  point  to  a  value  rather 
greater  than  1 8",  but  he  preferred  to  use  round  numbers.  The 
figures  at  present  accepted  are  l8"'42  ard  I3"75,  so  that  his  ellipse 
was  decidedly  less  flat  than  it  should  have  been. 

f  Recherches  sur  la  precession  des  equinoxes  et  sitr  la  nutation  de 
I'axe  de  la  terre. 


270  A  Short  History  of  Astronomy 

discoveries,  other  investigations  were  carried  out  by  him 
before  or  during  the  same  time. 

The  earliest  important  piece  of  work  which  he  accom- 
plished was  in  connection  with  Jupiter's  satellites.  His 
uncle  had  devoted  a  good  deal  of  attention  to  this  subject, 
and  had  drawn  up  some  tables  dealing  with  the  motion  of 
the  first  satellite,  which  were  based  on  those  of  Domenico 
Cassini,  but  contained  a  good  many  improvements.  Bradley 
seems  for  some  years  to  have  made  a  practice  of  frequently 
observing  the  eclipses  of  Jupiter's  satellites,  and  of  noting 
discrepancies  between  the  observations  and  the  tables  ;  and 
he  was  thus  able  to  detect  several  hitherto  unnoticed 
peculiarities  in  the  motions,  and  thereby  to  form  improved 
tables.  The  most  interesting  discovery  was  that  of  a 
period  of  437  days,  after  which  the  motions  of  the  three 
inner  satellites  recurred  with  the  same  irregularities. 
Bradley,  like  Pound,  made  use  of  Roemer's  suggestion 
(chapter  vin.,  §  162)  that  light  occupied  a  finite  time  in 
travelling  from  Jupiter  to  the  earth,  a  theory  which  Cassini 
and  his  school  long  rejected.  Bradley's  tables  of  Jupiter's 
satellites  were  embodied  in  Halley's  planetary  and  lunar 
tables,  printed  in  1719,  but  not  published  till  more  than 
30  years  afterwards  (§  204).  Before  that  date  the  Swedish 
astronomer  Pehr  Vilhelm  Wargentin  (17-17-1783)  had  in- 
dependently discovered  the  period  of  437  days,  which  he 
utilised  for  the  construction  of  an  extremely  accurate  set 
of  tables  for  the  satellites  published  in  1746. 

In  this  case  as  in  that  of  nutation  Bradley  knew  that  his 
mathematical  powers  were  unequal  to  giving  an  explanation 
on  gravitational  principles  of  the  inequalities  which  observa- 
tion had  revealed  to  him,  though  he  was  well  aware  of  the 
importance  of  such  an  undertaking,  and  definitely  expressed 
the  hope  "  that  some  geometer,*  in  imitation  of  the  great 
Newton,  would  apply  himself  to  the  investigation  of  these 
irregularities,  from  the  certain  and  demonstrative  principles 
of  gravity." 

On  the  other  hand,  he  made  in  1726  an  interesting 
practical  application  of  his  superior  knowledge  of  Jupiter's 

*  The  word  "geometer"  \\as  formerly  used,  as  "geometre"  still 
is  in  French,  in  the  wider  sense  in  which  "  mathematician  "  is  now 
customary, 


$$  2i7,  2x8]     Bradley 's  Minor   Work:  his  Observations     271 

satellites  by  determining,  in  accordance  with  Galilei's 
method  (chapter  vi.,  §  127),  but  with  remarkable  accuracy, 
the  longitudes  of  Lisbon  and  of  New  York. 

217.  Among    Bradley's    minor   pieces    of  work    may  be 
mentioned   his    observations    of    several    comets   and    his 
calculation  of  their  respective  orbits  according  to  Newton's 
method ;  the  construction  of  improved  tables  of  refraction, 
which  remained  in  use  for  nearly  a  century ;  a  share  in 
pendulum  experiments  carried  out  in  England  and  Jamaica 
with   the   object   of  verifying   the   variation    of  gravity   in 
different  latitudes  ;  a  careful  testing  of  Mayer's  lunar  tables 
(§  226),  together  with   improvements  of  them  ;  and  lastly, 
some  work  in  connection  with  the  reform  of  the  calendar 
made  in   1752  (cf.  chapter  n.,  §  22). 

218.  It  remains  to  give  some  account  of  the  magnificent 
series  of  observations  carried  out  during  Bradley's  adminis- 
tration of  the  Greenwich  Observatory. 

These  observations  fall  into  two  chief  divisions  of  unequal 
merit,  those  after  1749  having  been  made  with  some  more 
accurate  instruments  which  a  grant  from  the  government 
enabled  him  at  that  time  to  procure. 

The  main  work  of  the  Observatory  under  Bradley  con- 
sisted in  taking  observations  of  fixed  stars,  and  to  a  lesser 
extent  of  other  bodies,  as  they  passed  the  meridian,  the 
instruments  used  (the  "  mural  quadrant "  and  the  "  transit 
instrument ")  being  capable  of  motion  only  in  the  meridian, 
and  being  therefore  steadier  and  susceptible  of  greater 
accuracy  than  those  with  more  freedom  of  movement. 
The  most  important  observations  taken  during  the  years 
1750-1762,  amounting  to  about  60,000,  were  published  long 
after  Bradley's  death  in  two  large  volumes  which  appeared 
in  1798  and  1805.  A  selection  of  them  had  been  used 
earlier  as  the  basis  of  a  small  star  catalogue,  published  in 
the  Nautical  Almanac  for  1773;  but  it  was  not  till  1818 
that  the  publication  of  Bessel's  Fundamenta  Astronomiae 
(chapter  XIIL,  §  277),  a  catalogue  of  more  than  3000  stars 
based  on  Bradley's  observations,  rendered  these  observations 
thoroughly  available  for  astronomical  work.  One  reason 
for  this  apparently  excessive  delay  is  to  be  found  in 
Bradley's  way  of  working.  Allusion  has  already  been 
made  to  a  variety  of  causes  which  prevent  the  apparent 


272  A  Short  History  of  Astronomy  [Cn.  x. 

place  of  a  star,  as  seen  in  the  telescope  and  noted  at  the 
time,  from  being  a  satisfactory  permanent  record  of  its 
position.  There  are  various  instrumental  errors,  and  errors 
due  to  refraction ;  again,  if  a  star's  places  at  two  different 
times  are  to  be  compared,  precession  must  be  taken  into 
account ;  and  Bradley  himself  unravelled  in  aberration  and 
nutation  two  fresh  sources  of  error.  In  order  therefore 
to  put  into  a  form  satisfactory  for  permanent  reference  a 
number  of  star  observations,  it  is  necessary  to  make  cor- 
rections which  have  the  effect  of  allowing  for  these  various 
sources  of  error.  This  process  of  reduction,  as  it  is  techni- 
cally called,  involves  a  certain  amount  of  rather  tedious 
calculation,  and  though  in  modern  observatories  the  process 
has  been  so  far  systematised  that  it  can  be  carried  out 
almost  according  to  fixed  rules  by  comparatively  unskilled 
assistants,  in  Bradley's  time  it  required  more  judgment, 
and  it  is  doubtful  if  his  assistants  could  have  performed 
the  work  satisfactorily,  even  if  their  time  had  not  been  fully 
occupied  with  other  duties.  Bradley  himself  probably 
found  the  necessary  calculations  tedious,  and  preferred 
devoting  his  energies  to  work  of  a  higher  order.  It  is 
true  that  Delambre,  the  famous  French  historian  of 
astronomy,  assures  his  readers  that  he  had  never  found 
the  reduction  of  an  observation  tedious  if  performed  the 
same  day,  but  a  glance  at  any  of  his  books  is  enough  to 
shew  his  extraordinary  fondness  for  long  calculations  of 
a  fairly  elementary  character,  and  assuredly  Bradley  is  not 
the  only  astronomer  whose  tastes  have  in  this  respect 
differed  fundamentally  from  Delambre's.  Moreover  reducing 
an  observation  is  generally  found  to  be  a  duty  that,  like 
answering  letters,  grows  harder  to  perform  the  longer  it 
is  neglected ;  and  it  is  not  only  less  interesting  but  also 
much  more  difficult  for  an  astronomer  to  deal  satisfactorily 
with  some  one  else's  observations  than  with  his  own.  It 
is  not  therefore  surprising  that  after  Bradley's  death  a 
long  interval  should  have  elapsed  before  an  astronomer 
appeared  with  both  the  skill  and  the  patience  necessary 
for  the  complete  reduction  of  Bradley's  60,000  observations. 
A  variety  of  circumstances  combined  to  make  Bradley's 
observations  decidedly  superior  to  those  of  his  predecessors. 
He  evidently  possessed  in  a  marked  degree  the  personal 


S  219]  Bradley 's  Observations  273 

characteristics — of  eye  and  judgment — which  make  a  first- 
rate  observer ;  his  instruments  were  mounted  in  the  best 
known  way  for  securing  accuracy,  and  were  constructed  by 
the  most  skilful  makers  ;  he  made  a  point  of  studying  very 
carefully  the  defects  of  his  instruments,  and  of  allowing 
for  them ;  his  discoveries  of  aberration  and  nutation 
enabled  him  to  avoid  sources  of  error,  amounting  to  a 
considerable  number  of  seconds,  which  his  predecessors 
could  only  have  escaped  imperfectly  by  taking  the  average 
of  a  number  of  observations ;  and  his  improved  tables  of 
refraction  still  further  added  to  the  correctness  of  his 
results. 

Bessel  estimates  that  the  errors  in  Bradley's  observations 
of  the  declination  of  stars  were  usually  less  than  4",  while 
the  corresponding  errors  in  right  ascension,  a  quantity  which 
depends  ultimately  on  a  time-observation,  were  less  than  15", 
or  one  second  of  time.  His  observations  thus  shewed  a 
considerable  advance  in  accuracy  compared  with  those  of 
Flamsteed  (§  198),  which  represented  the  best  that  had 
hitherto  been  done. 

219.  The  next  Astronomer  Royal  was  Nathaniel  Bliss 
(1700-1764),  who  died  after  two  years.  He  was  in  turn 
succeeded  by  Nevil  Maskelyne  (1732-1811),  who  carried 
on  for  nearly  half  a  century  the  tradition  of  accurate 
observation  which  Bradley  had  established  at  Greenwich, 
and  made  some  improvements  in  methods. 

To  him  is  also  due  the  first  serious  attempt  to  measure 
the  density  and  hence  the  mass  of  the  earth.  By  com- 
paring the  attraction  exerted  by  the  earth  with  that  of 
the  sun  and  other  bodies,  Newton,  as  we  have  seen 
(chapter  ix.,  §  185),  had  been  able  to  connect  the  masses 
of  several  of  the  celestial  bodies  with  that  of  the  earth. 
To  connect  the  mass  of  the  whole  earth  with  that  of  a 
given  terrestrial  body,  and  so  express  it  in  pounds  or  tons, 
was  a  problem  of  quite  a  different  kind.  It  is  of  course 
possible  to  examine  portions  of  the  earth's  surface  and 
compare  their  density  with  that  of,  say,  water ;  then  to 
make  some  conjecture,  based  on  rough  observations  in 
mines,  etc.,  as  to  the  rate  at  which  density  increases  as 
we  go  from  the  surface  towards  the  centre  of  the  earth, 
and  hence  to  infer  the  average  density  of  the  earth.  Thus 

18 


274  ^  Short  History  of  Astronomy  [LH.  x. 

the  mass  of  the  whole  earth  is  compared  with  that  of  a 
globe  of  water  of  the  same  size,  and,  the  size  being  known, 
is  expressible  in  pounds  or  tons. 

By  a  process  of  this  sort  Newton  had  in  fact,  with  extra- 
ordinary insight,  estimated  that  the  density  of  the  earth 
was  between  five  and  six  times  as  great  as  that  of  water.* 

It  was,  however,  clearly  desirable  to  solve  the  problem 
in  a  less  conjectural  manner,  by  a  direct  comparison  of 
the  gravitational  attraction  exerted  by  the  earth  with  that 
exerted  by  a  known  mass — a  method  that  would  at  the 
same  time  afford  a  valuable  test  of  Newton's  theory  of  the 
gravitating  properties  of  portions  of  the  earth,  as  distinguished 
from  the  whole  earth.  In  their  Peruvian  expedition  (§  221), 
Bouguer  and  La  Condamine  had  noticed  certain  small  deflec- 
tions of  the  plumb-line,  which  indicated  an  attraction  by 
Chimborazo,  near  which  they  were  working ;  but  the  obser- 
vations were  too  uncertain  to  be  depended  on.  Maskelyne 
selected  for  his  purpose  Schehallien  in  Perthshire,  a  narrow 
ridge  running  east  and  west.  The  direction  of  the  plumb- 
line  was  observed  (1774)  on  each  side  of  the  ridge,  and 
a  change  in  direction  amounting  to  about  12"  was  found 
to  be  caused  by  the  attraction  of  the  mountain.  As  the 
direction  of  the  plumb-line  depends  on  the  attraction  of 
the  earth  as  a  whole  and  on  that  of  the  mountain,  this 
deflection  at  once  led  to  a  comparison  of  the  two  attrac- 
tions. Hence  an  intricate  calculation  performed  by  Charles 
Hutton  (1737-1823)  led  to  a  comparison  of  the  average 
densities  of  the  earth  and  mountain,  and  hence  to  the  final 
conclusion  (published  in  1778)  that  the  earth's  density  was 
about  4|  times  that  of  water.  As  Mutton's  estimate  of  the 
density  of  the  mountain  was  avowedly  almost  conjectural, 
this  result  was  of  course  correspondingly  uncertain. 

A  few  years  \a.tei John  Michell  (1724-1793)  suggested,  and 
the  famous  chemist  and  electrician  Henry  Cavendish  (1731- 
1810)  carried  out  (1798),  an  experiment  in  which  the 
mountain  was  replaced  by  a  pair  of  heavy  balls,  and  their 
attraction  on  another  body  was  compared  with  that  of  the 
earth,  the  result  being  that  the  density  of  the  earth  was 
found  to  be  about  5^  times  that  of  water. 

*  Prtncipta,  Book  III.,  proposition  10. 


§5  220,  2  i]  The  Density  of  the  Earth  275 

The  Cavendish  experiment,  as  it  is  often  called,  has 
since  been  repeated  by  various  other  experimenters  in 
modified  forms,  and  one  or  two  other  methods,  too  technical 
to  be  described  here,  have  also  been  devised.  All  the 
best  modern  experiments  give  for  the  density  numbers 
converging  closely  on  5^,  thus  verifying  in  a  most  striking 
way  both  Newton's  conjecture  and  Cavendish's  original 
experiment. 

With  this  value  of  the  density  the  mass  of  the  earth  is 
a  little  more  than  13  billion  billion  pounds,  or  more 
precisely  13,136,000,000,000,000,000,000,000  Ibs. 

220.  While  Greenwich  was  furnishing  the  astronomical 
world  with  a  most  valuable  series  of  observations,  the  Paris 
Observatory  had  not  fulfilled   its  early  promise.     It  was 
in  fact  suffering,  like  English  mathematics,  from  the  evil 
effects  of  undue  adherence  to  the  methods  and  opinions  of 
a  distinguished  man.     Domenico  Cassini  happened  to  hold 
several    erroneous    opinions    in     important     astronomical 
matters ;  he   was   too  go6d   a   Catholic   to   be  a  genuine 
Coppernican,  he  had  no  belief  in  gravitation,  he  was  firmly 
persuaded  that  the  earth  was  flattened  at  the  equator  instead 
of  at  the  poles,  and  he  rejected  Roemer's  discovery  of  the 
velocity  of  light.     After  his  death  in  1712  the  directorship 
of  the  Observatory  passed  in  turn  to  three  of  his  descendants, 
the   last  of  whom   resigned   office   in    1793;  and   several 
members  of  the  Maraldi  family,  into  which  his  sister  had 
married,  worked  in  co-operation  with  their  cousins.     Un- 
fortunately a  good  deal  of  their  energy  was  expended,  first 
in  defending,  and  afterwards  in  gradually  withdrawing  from, 
the  errors  of  their  distinguished  head.    Jacques  Cassini,  for 
example,  the  second  of  the  family  (1677-1756),  although 
a  Coppernican,  was  still  a  timid  one,  and  rejected  Kepler's 
law  of  areas ;  his  son  again,  commonly  known  as  Cassini  de 
Thury  (1714-1784),  still  defended  the  ancestral  errors  as 
to  the  form  of  the  earth  ;  while  the  fourth  member  of  the 
family,    Count  Cassini  (1748-1845),  was   the   first   of  the 
family  to  accept  the  Newtonian  idea  of  gravitation. 

Some  planetary  and  other  observations  of  value  were 
made  by  the  Cassini-Maraldi  school,  but  little  of  this  work 
was  of  first-rate  importance. 

221.  A  series  of  important  measurements  of  the  earth, 


276  A  Short  History  of  Astronomy  [CH.  x. 

in  which  the  Cassinis  had  a  considerable  share,  were  made 
during  the  i8th  century,  almost  entirely  by  Frenchmen, 
and  resulted  in  tolerably  exact  knowledge  of  the  earth's 
size  and  shape. 

The  variation  of  the  length  of  the  seconds  pendulum 
observed  by  Richer  in  his  Cayenne  expedition  (chapter  vin., 
§  161)  had  been  the  first  indication  of  a  deviation  of  the 
earth  from  a  spherical  form.  Newton  inferred,  both  from 
these  pendulum  experiments  and  from  'an  independent 
theoretical  investigation  (chapter  ix.,  §  187),  that  the  earth 
was  spheroidal,  being  flattened  towards  the  poles ;  and 
this  view  was  strengthened  by  the  satisfactory  explanation 
of  precession  to  which  it  led  (chapter  ix.,  §  188). 

On  the  other  hand,  a  comparison  of  various  measurements 
of  arcs  of  the  meridian  in  different  latitudes  gave  some 
support  to  the  view  that  the  earth  was  elongated  towards 
the  poles  and  flattened  towards  the  equator,  a  view  cham- 
pioned with  great  ardour  by  the  Cassini  school.  It  was 
clearly  important  that  the  question  should  be  settled  by 
more  extensive  and  careful  earth-measurements. 

The  essential  part  of  an  ordinary  measurement  of  the 
earth  consists  in  ascertaining  the  distance  in  miles  between 
two  places  on  the  same  meridian,  the  latitudes  of  which 
differ  by  a  known  amount.  From  these  two  data  the  length 
of  an  arc  of  a  meridian  corresponding  to  a  difference  of 
latitude  of  i°  at  once  follows.  The  latitude  of  a  place  is 
the  angle  which  the  vertical  at  the  place  makes  with  the 
equator,  or,  expressed  in  a  slightly  different  form,  is  the 
angular  distance  of  the  zenith  from  the  celestial  equator. 
The  vertical  at  any  place  may  be  defined  as  a  direction 
perpendicular  to  the  surface  of  still  water  at  the  place  in 
question,  and  may  be  regarded  as  perpendicular  to  the 
true  surface  of  the  earth,  accidental  irregularities  in  its  form 
such  as  hills  and  valleys  being  ignored.* 

The  difference  of  latitude  between  two  places,  north  and 
south  of  one  another,  is  consequently  the  angle  between 
the  verticals  there.  Fig.  78  shews  the  verticals,  marked 
by  the  arrowheads,  at  places  on  the  same  meridian  in 

*  It  is  important  for  the  purposes  of  this  discussion  to  notice  that 
the  vertical  is  not  the  lin^  drawn  from  the  centre  of  the  earth  .to  tjie 
place  of  observation. 


121] 


The  Shape  of  the  Earth 


277 


latitudes  differing  by  10°;  so  that  two  consecutive  verticals 
are  inclined  in  every  case  at  an  angle  of  10°. 

If,  as  in  fig.  78,  the  shape  of  the  earth  is  drawn  in  accord- 
ance with  Newton's  views,  the  figure  shews  at  once  that 
the  arcs  A  A,,  A,  A2,  etc.,  each  of  which  corresponds  to  10°  of 
latitude,  steadily  increase  as  we  pass  from  a  point  A  on  the 
equator  to  the  pole  B.  If  the  opposite  hypothesis  be 


i  FIG.  78. — The  varying  curvature  of  the  earth. 

adopted,  which  will  be  illustrated  by  the  same  figure  if  we 
now  regard  A  as  the  pole  and  B  as  a  point  on  the  equator, 
then  the  successive  arcs  decrease  as  we  pass  from  equator 
to  pole.  A  comparison  of  the  measurements  made  by 
Eratosthenes  in  Egypt  (chapter  n.,  §  36)  with  some  made 
in  Europe  (chapter  VIIL,  §  159)  seemed  to  indicate  that  a 
degree  of  the  meridian  near  the  equator  was  longer  than 
one  in  higher  latitudes  ;  and  a  similar  conclusion  was  in- 
dicated by  a  comparison  of  different  portions  of  an  extensive 


278  A  Short  History  of  Astronomy  [CH.  x. 

French  arc,  about  9°  in  length,  extending  from  Dunkirk 
to  the  Pyrenees,  which  was  measured  under  the  super- 
intendence of  the  Cassinis  in  continuation  of  Picard's  arc, 
the  result  being  published  by  J.  Cassini  in  1720.  In 
neither  case,  however,  were  the  data  sufficiently  accurate  to 
justify  the  conclusion ;  and  the  first  decisive  evidence  was 
obtained  by  measurement  of  arcs  in  places  differing  far 
more  widely  in  latitude  than  any  that  had  hitherto  been 
available.  The  French  Academy  organised  an  expedition 
to  Peru,  under  the  management  of  three  Academicians, 
Pierre  Bouguer  (1698-1758),  Charles  Marie  de  La  Conda- 
mine  (1701-1774),  and  Louis  Godin  (1704-1760),  with 
whom  two  Spanish  naval  officers  also  co-operated. 

The  expedition  started  in  1735,  an^5  owing  to  various 
difficulties,  the  work  was  spread  out  over  nearly  ten  years. 
The  most  important  result  was  the  measurement,  with  very 
fair  accuracy,  of  an  arc  of  about  3°  in  length,  close  to  the 
equator ;  but  a  number  of  pendulum  experiments  of  value 
were  also  performed,  and  a  good  many  miscellaneous 
additions  to  knowledge  were  made. 

But  while  the  Peruvian  party  were  still  at  their  work  a 
similar  expedition  to  Lapland,  under  the  Academician1 
Pierre  Louis  Moreau  de  Maupertuis  (1698-1759),  had  much 
more  rapidly  (1736-7),  if  somewhat  carelessly,  effected  the 
measurement  of  an  arc  of  nearly  i°  close  to  the  arctic  circle. 

From  these  measurements  it  resulted  that  the  lengths 
of  a  degree  of  a  meridian  about  latitude  2°  S.  (Peru), 
about  latitude  47°  N.  (France)  and  about  latitude  66°  N. 
(Lapland)  were  respectively  362,800  feet,  364,900  feet,  and 
367,100  feet.*  There  was  therefore  clear  evidence,  from 
a  comparison  of  any  two  of  these  arcs,  of  an  increase  of 
the  length  of  a  degree  of  a  meridian  as  the  latitude  increases ; 
and  the  general  correctness  of  Newton's  views  as  against 
Cassini's  was  thus  definitely  established. 

The  extent  to  which  the  earth  deviates  from  a  sphere 
is  usually  expressed  by  a  fraction  known  as  the  ellipticity, 
which  is  the  difference  between  the  lines  c  A,  c  B  of  fig.  78 
divided  by  the  greater  of  them.  From  comparison  of  the 
three  arcs  just  mentioned  several  very  different  values  of  the 

*  69  miles  is  364.320  feet,  so  that  the  two  northern  degrees  were 
a  little  more  and  the  Peruvian  are  a  little  less  than  69  miK  s 


§  222]  The  Shape  of  the  Earth  279 

ellipticity  were  deduced,  the  discrepancies  being  partly  due 
to  different  theoretical  methods  of  interpreting  the  results 
and  partly  to  errors  in  the  arcs. 

A  measurement,  made  by  Jons  Svanberg  (1771-1851)  in 
1801-3,  of  an  arc  near  that  of  Maupertuis  has  in  fact 
shewn  that  his  estimate  of  the  length  of  a  degree  was 
about  1,000  feet  too  large. 

A  large  number  of  other  arcs  have  been  measured  in 
different  parts  of  the  earth  at  various  times  during  the 
1 8th  and  igth  centuries.  The  details  of  the  measurements 
need  not  be  given,  but  to  prevent  recurrence  to  the  subject 
it  is  convenient  to  give  here  the  results,  obtained  by  a 
comparison  of  these  different  measurements,  that  the 
ellipticity  is  very  nearly  ^ \^  and  the  greatest  radius  of  the 
earth  (c  A  in  fig.  78)  a  little  less  than  21,000,000  feet  or 
4,000  miles.  It  follows  from  these  figures  that  the  length 
of  a  degree  in  the  latitude  of  London  contains,  to  use  Sir 
John  Herschel's  ingenious  mnemonic,  almost  exactly  as 
many  thousand  feet  as  the  year  contains  days. 

222.  Reference  has  already  been  made  to  the  supremacy 
of  Greenwich  during  the  i8th  century  in  the  domain  of 
exact  observation.  France,  however,  produced  during  this 
period  one  great  observing  astronomer  who  actually  accom- 
plished much,  and  under  more  favourable  external  conditions 
might  almost  have  rivalled  Bradley. 

Nicholas  Louis  de  Lacaille  was  born  in  1713.  After  he 
had  devoted  a  good  deal  of  time  to  theological  studies 
with  a  view  to  an  ecclesiastical  career,  his  interests  were 
diverted  to  astronomy  and  mathematics.  He  was  intro- 
duced to  Jacques  Cassini,  and  appointed  one  of  the 
assistants  at  the  Paris  Observatory. 

In  1738  and  the  two  following  years  he  took  an  active 
part  in  the  measurement  of  the  French  arc,  then  in  process 
of  verification.  While  engaged  in  this  work  he  was  ap- 
pointed (1739)  to  a  poorly  paid  professorship  at  the 
Mazarin  College,  at  which  a  small  observatory  was  erected. 
Here  it  was  his  regular  practice  to  spend  the  whole  night, 
if  fine,  in  observation,  while  "  to  fill  up  usefully  the  hours 
of  leisure  which  bad  weather  gives  to  observers  only  too 
often  "  he  undertook  a  variety  of  extensive  calculations  and 
wrote  innumerable  scientific  memoirs.  It  is  therefore  not 


280  A  Short  History  of  Astronomy  [CH.  x. 

surprising  that  he  died  comparatively  early  (1762)  and  that 
his  death  was  generally  attributed  to  Overwork. 

223.  The  monotony  of  Lacaille's  outward  life  was  broken 
by  the  scientific  expedition  to  the  Cape  of  Good  Hope 
(1750-1754)  organised  by  the  Academy  of  Sciences  and 
placed  under  his  direction. 

The  most  striking  piece  of  work  undertaken  during  this 
expedition  was  a  systematic  survey  of  the  southern  skies, 
in  the  course  of  which  more  than  10,000  stars  were 
observed. 

These  observations,  together  with  a  carefully  executed 
catalogue  of  nearly  2,000  of  the  stars  *  and  a  star-map,  were 
published  posthumously  in  1763  under  the  title  Coelum 
Australe  Stelliferum^  and  entirely  superseded  Halley's  much 
smaller  and  less  accurate  catalogue  (§  199).  Lacaille 
found  it  necessary  to  make  14  new  constellations  (some 
of  which  have  since  been  generally  abandoned),  and  .to 
restore  to  their  original  places  the  stars  which  the  loyal 
Halley  had  made  into  King  Charles's  Oak.  Incidentally 
Lacaille  observed  and  described  42  nebulae,  nebulous  stars, 
and  star-clusters,  objects  the  systematic  study  of  which 
was  one  of  Herschel's  great  achievements  (chapter  xn., 
§§  259-261). 

He  made  a  large  number  of  pendulum  experiments,  at 
Mauritius  as  well  as  at  the  Cape,  with  the  usual  object  of 
determining  in  a  new  part  of  the  world  the  acceleration 
due  to  gravity,  and  measured  an  arc  of  the  meridian  ex- 
tending over  rather  more  than  a  degree.  He  made  also 
careful  observations  of  the  positions  of  Mars  and  Venus, 
in  order  that  from  comparison  of  them  with  simultaneous 
observations  in  northern  latitudes  he  might  get  the  parallax 
of  the  sun  (chapter  vin.,  §  161).  These  observations  of 
Mars  compared  with  some  made  in  Europe  by  Bradley  and 
others,  and  a  similar  treatment  of  Venus,  both  pointed  to 
a  solar  parallax  slightly  in  excess  of  10",  a  result  less 
accurate  than  Cassini's  (chapter  vin.,  §  161),  though 
obtained  by  more  reliable  processes. 

A  large  number  of  observations  of  the  moon,  of  which 

*  The  remaining  8,000  stars  were  not  "  reduced "  by  Lacaille. 
The  whole  number  were  first  published  in  the  "reduced"  form  by 
the  British  Association  in  1845. 


$5  223,  224]  Lacaille  281 

those  made  by  him  at  the  Cape  formed  an  important  part, 
led,  after  an  elaborate  discussion  in  which  the  spheroidal 
form  of  the  earth  was  taken  into  account,  to  an  improved 
value  of  the  moon's  distance,  first  published  in  1761. 

Lacaille  also  used  his  observations  of  fixed  stars  to 
improve  our  knowledge  of  refraction,  and  obtained  a 
number  of  observations  of  the  sun  in  that  part  of  its  orbit 
which  it  traverses  in  our  winter  months  (the  summer  cf 
the  southern  hemisphere),  and  in  which  it  is  therefore 
too  near  the  horizon  to  be  observed  satisfactorily  in 
Europe. 

The  results  of  this — one  of  the  most  fruitful  scientific 
expeditions  ever  undertaken — were  published  in  separate 
memoirs  or  embodied  in  various  books  published  after  his 
return  to  Paris. 

224.  In  1757,  under  the  title  Astronomiae  Fundamenta, 
appeared  a  catalogue  of  400  of  the  brightest  stars,  observed 
and  reduced  with  the  most  scrupulous  care,  so  that,  not- 
withstanding the  poverty  of  Lacaille's  instrumental  outfit, 
the  catalogue  was  far  superior  to  any  of  its  predecessors, 
and  was  only  surpassed  by  Bradley's  observations  as  they 
were  gradually  published.  It  is  characteristic  of  Lacaille's 
unselfish  nature  that  he  did  not  have  the  Fundamenta  sold 
in  the  ordinary  way,  but  distributed  copies  gratuitously  to 
those  interested  in  the  subject,  and  earned  the  money 
necessary  to  pay  the  expenses  of  publication  by  calculating 
some  astronomical  almanacks. 

Another  catalogue,  of  rather  more  than  500  stars  situated 
in  the  zodiac,  was  published  posthumously. 

In  the  following  year  (1758)  he  published  an  excellent 
set  of  Solar  Tables,  based  on  an  immense  series  of  observa- 
tions and  calculations.  These  were  remarkable  as  the  first 
in  which  planetary  perturbations  were  taken  into  account. 

Among  Lacaille's  minor  contributions  to  astronomy  may 
be  mentioned  :  improved  methods  of  calculating  cometary 
orbits  and  the  actual  calculation  of  the  orbits  of  a  large 
number  of  recorded  comets,  the  calculation  of  all  eclipses 
visible  in  Europe  since  the  year  i,  a  warning  that  the 
transit  of  Venus  would  be  capable  of  far  less  accurate 
observation  than  Halley  had  expected  (§  202),  observations 
of  the  actual  transit  of  1761  (§227),  and  a  number  of 


282  A  Short  History  of  Astronomy  u...  x. 

improvements  in  methods   of  calculation  and  of  utilising 
observations. 

In  estimating  the  immense  mass  of  work  which  Lacaille 
accomplished  during  an  astronomical  career  of  about  22 
years,  it  has  also  to  be  borne  in  mind  that  he  had  only 
moderately  good  instruments  at  his  observatory,  and  no 
assistant^  and  that  a  considerable  part  of  his  time  had  to 
be  spent  in  earning  the  means  of  living  and  of  working. 

225.  During   the   period   under   consideration  Germany 
also  produced  one  astronomer,    primarily  an  observer,  of 
great  merit,  Tobias  Mayer  (1723-1762).    He  was  appointed 
professor  of  mathematics  and  political  economy  at  Gottingeu 
in  1751,  apparently  on  the  understanding  that  he  need  not 
lecture  on  the  latter  subject,  of  which  indeed  he  seems 
to  have  professed  no  knowledge ;  three  years  later  he  was 
put  in  charge  of  the  observatory,  which  had  been  erected 
20   years  before.     He  had  at  least  one  fine  instrument,* 
and  following  the  example  of  Tycho,  Flamsteed,  and  Bradley, 
he  made  a  careful  study  of  its  defects,  and  carried  further 
than   any   of  his   predecessors   the    theory    of    correcting 
observations  for  instrumental  errors. t 

He  improved  Lacaille's  tables  of  the  sun,  and  made  a 
catalogue  of  998  zodiacal  stars,  published  posthumously  in 
1775  ;  by  a  comparison  of  star  places  recorded  by  Roemer 
(1706)  with  his  own  and  Lacaille's  observations  he  obtained 
evidence  of  a  considerable  number  of  proper  motions 
(§  203) ;  and  he  made  a  number  of  other  less  interesting 
additions  to  astronomical  knowledge. 

226.  But  Mayer's  most  important  work  was  on  the  moon. 
At  the  beginning  of  his  career  he  made  a  careful  study  of 
the  position  of  the  craters  and  other  markings,  and  was 
thereby  able  to  get  a  complete  geometrical  explanation  of 
the  various  librations  of  the  moon  (chapter  vi.,  §  133),  and 
to  fix  with  accuracy  the  position  of  the  axis  about  which 
the  moon  rotates.      A  map   of  the   moon    based   on   his 
observations  was  published  with  other  posthumous  works 
in  1775. 

*  A  mural  quadrant. 

f  The  ordinary  approximate  theory  of  the  collimation  error,  level 
error,  and  deviation  error  of  a  transit,  as  given  in  text-books  of 
spherical  and  practical  astronomy,  is  substantially  his. 


FIG.  79. — Tobias  Mayer's  map  of  the  moon. 


[To  face  p.  282. 


$§  225,  226]  Tobias  Mayer  283 

Much  more  important,  however,  were  his  lunar  theory 
and  the  tables  based  on  it.  The  intrinsic  mathematical 
interest  of  the  problem  of  the  motion  of  the  moon,  and  its 
practical  importance  for  the  determination  of  longitude,  had 
caused  a  great  deal  of  attention  to  be  given  to  the  subject 
by  the  astronomers  of  the  i8th  century.  A  further  stimulus 
was  also  furnished  by  the  prizes  offered  by  the  British 
Government  in  1713  for  a  method  of  finding  the  Longitude 
at  sea,  viz.  ,£20,000  for  a  method  reliable  to  within  half 
a  degree,  and  smaller  amounts  for  methods  of  less  accuracy. 

All  the  great  mathematicians  of  the  period  made  attempts 
at  deducing  the  moon's  motions  from  gravitational  principles. 
Mayer  worked  out  a  theory  in  accordance  with  methods 
used  by  Euler  (chapter  XL,  §  233),  but  made  a  much  more 
liberal  and  also  more  skilful  use  of  observations  to  determine 
various  numerical  quantities,  which  pure  theory  gave  either 
not  at  all  or  with  considerable  uncertainty.  He  accordingly 
succeeded  in  calculating  tables  of  the  moon  (published  with 
those  of  the  sun  in  1753)  which  were  a  notable  improve- 
ment on  those  of  any  earlier  writer.  After  making  further 
improvements,  he  sent  them  in  1755  to  England.  Bradley, 
to  whom  the  Admiralty  submitted  them  for  criticism,  re- 
ported favourably  of  their  accuracy ;  and  a  few  years  later, 
after  making  some  alterations  in  the  tables  on  the  basis  of 
his  own  observations,  he  recommended  to  the  Admiralty  a 
longitude  method  based  on  their  use  which  he  estimated 
to  be  in  general  capable  of  giving  the  longitude  within 
about  half  a  degree. 

Before  anything  definite  was  done,  Mayer  died  at  the 
early  age  of  39,  leaving  behind  him  a  new  set  of  tables, 
which  were  also  sent  to  England.  Ultimately  ,£3,000  was 
paid  to  his  widow  in  1765  ;  and  both  his  Theory  of  the 
Moon*  and  his  improved  Solar  and  Lunar  Tables  were 
published  in  1770  at  the  expense  of  the  Board  of  Longitude. 
A  later  edition,  improved  by  Bradley's  former  assistant 
Charles  Mason  (1730-1787),  appeared  in  1787. 

A  prize  was  also  given  to  Euler  for  his  theoretical  work ; 
while  £3,000  and  subsequently  £10,000  more  were  awarded 
to  John  Harrison  for  improvements  in  the  chronometer, 

*  The  title-page  is  dated  1767;  but  it  is  known  not  to  have  been 
actually  published  till  three  years  later. 


284  A  Short  History  of  Astronomy  [CH.  x. 

which  rendered  practicable  an  entirely  different  method 
of  finding  the  longitude  (chapter  vi.,  §  127). 

227.  The  astronomers  of  the  i8th  century  had  two 
opportunities  of  utilising  a  transit  of  Venus  for  the  deter- 
mination of  the  distance  of  the  sun,  as  recommended  by 
Halley  (§  202). 

A  passage  or  transit  of  Venus  across  the  sun's  disc  is 
a  phenomenon  of  the  same  nature  as  an  eclipse  of  the 
sun  by  the  moon,  with  the  important  difference  that  the 
apparent  magnitude  of  the  planet  is  too  small  to  cause  any 
serious  diminution  in  the  sun's  light,  and  it  merely  appears 
as  a  small  black  dot  on  the  bright  surface  of  the  sun. 

If  the  path  of  Venus  lay  in  the  ecliptic,  then  at  every 
inferior  conjunction,  occurring  once  in  584  days,  she  would 
necessarily  pass  between  the  sun  and  earth  and  would 
appear  to  transit.  As,  however,  the  paths  of  Venus  and  the 
earth  are  inclined  to  one  another,  at  inferior  conjunction 
Venus  is  usually  far  enough  "  above "  or  "  below  "  the 
ecliptic  for  no  transit  to  occur.  With  the  present  position 
of  the  two  paths — which  planetary  perturbations  are  only 
very  gradually  changing — transits  of  Venus  occur  in  pairs 
eight  years  apart,  while  between  the  latter  of  one  pair  and 
the  earlier  of  the  next  pair  elapse  alternately  intervals  of 
105!  and  of  i2i|  years.  Thus  transits  have  taken  place  in 
December  1631  and  1639,  June  1761  and  1769,  December 
1874  and  1882,  and  will  occur  again  in  2004  and  2012, 
2117  and  2125,  and  so  on. 

The  method  of  getting  the  distance  of  the  sun  from  a 
transit  of  Venus  may  be  said  not  to  differ  essentially  from 
that  based  on  observations  of  Mars  (chapter  vni.,  §  161). 

The  observer's  object  in  both  cases  is  to  obtain  the 
difference  in  direction  of  the  planet  as  seen  from  different 
places  on  the  earth.  Venus,  however,  when  at  all  near 
the  earth,  is  usually  too  near  the  sun  in  the  sky  to  be 
capable  of  minutely  exact  observation,  but  when  a  transit 
occurs  the  sun's  disc  §erves  as  it  were  as  a  dial-plate  on 
which  the  position  of  the  planet  can  be  noted.  Moreover 
the  measurement  of  minute  angles,  an  art  not  yet  carried 
to  very  great  perfection  in  the  i8th  century,  can  be  avoided 
by  time-observations,  as  the  difference  in  the  times  at 
which  Venus  enters  (or  leaves)  the  sun's  disc  as  seen  at 


$  227]  Transits  of  Venus  285 

different  stations,  or  the  difference  in  the  durations  of  the 
transit,  can  be  without  difficulty  translated  into  difference 
of  direction,  and  the  distances  of  Venus  and  the  sun  can 
be  deduced.* 

Immense  trouble  was  taken  by  Governments,  Academies, 
and  private  persons  in  arranging  for  the  observation  of  the 
transits  of  1761  and  1769.  For  the  former  observing 
parties  were  sent  as  far  as  to  Tobolsk,  St.  Helena,  the 
Cape  of  Good  Hope,  and  India,  while  observations  were 
also  made  by  astronomers  at  Greenwich,  Paris,  Vienna, 
Upsala,  and  elsewhere  in  Europe.  The  next  transit  was 
observed  on  an  even  larger  scale,  the  stations  selected 
ranging  from  Siberia  to  California,  from  the  Varanger  Fjord 
to  Otaheiti  (where  no  less  famous  a  person  than  Captain 
Cook  was  placed),  and  from  Hudson's  Bay  to  Madras. 

The  expeditions  organised  on  this  occasion  by  the 
American  Philosophical  Society  may  be  regarded  as  the 
first  of  the  contributions  made  by  America  to  the  science 
which  has  since  owed  so  much  to  her ;  while  the  Empress 
Catherine  bore  witness  to  the  newly  acquired  civilisation  of 
her  country  by  arranging  a  number  of  observing  stations 
on  Russian  soil. 

The  results  were  far  more  in  accordance  with  Lacaille's 
anticipations  than  with  Halley's.  A  variety  of  causes  pre- 
vented the  moments  of  contact  between  the  discs  of  Venus 
and  the  sun  from  being  observed  with  the  precision  that 
had  been  hoped.  By  selecting  different  sets  of  observations, 
and  by  making  different  allowances  for  the  various  probable 
sources  of  error,  a  number  of  discordant  results  were 
obtained  by  various  calculators.  The  values  of  the  parallax 
(chapter  vin.,  §  161)  of  the  sun  deduced  from  the  earlier 
of  the  two  transits  ranged  between  about  8"  and  10";  while 
those  obtained  in  1769,  though  much  more  consistent,  still 
varied  between  about  8"  and  9",  corresponding  to  a  variation 
of  about  10,000,000  miles  in  the  distance  of  the  sun. 

The  whole  set  of  observations  were  subsequently  very 
elaborately  discussed  in  1822-4  and  again  in  1835  by 
Johann  Franz  Encke  (1791-1865),  who  deduced  a  parallax 
of  8"'57i,  corresponding  to  a  distance  of  95,370,000  miles, 

*  For  a  more  detailed  discussion  of  the  transit  of  Venus,  see  Airy's 
Popular  Astronomy  and  Newcomb's  Popular  Astroriomv, 


286  A  Short  History  of  Astrcnomy       [CH.  x.,  §  2  7 

a  number  which  long  remained  classical.  The  uncertainty 
of  the  data  is,  however,  shewn  by  the  fact  that  other  equally 
competent  astronomers  have  deduced  from  the  observations 
of  1769  parallaxes  of  8"'8  and  8"'9. 

No  account  has  yet  been  given  of  William  Herschel, 
perhaps  the  most  famous  of  all  observers,  whose  career 
falls  mainly  into  the  last  quarter  of  the  i8th  century  and 
the  earlier  part  of  the  iQth  century.  As,  however,  his 
work  was  essentially  different  from  that  of  almost  all  the 
astronomers  of  the  i8th  century,  and  gave  a  powerful 
impulse  to  a  department  of  astronomy  hitherto  almost 
ignored,  it  is  convenient  to  postpone  to  a  later  chapter  (xn.) 
the  discussion  of  his  work 


CHAPTER   XI. 

GRAVITATIONAL   ASTRONOMY    IN    THE    l8TH    CENTURY. 

"Astronomy,  considered  in  the  most  general  way,  is  a  great  problem 
of  mechanics,  the  arbitrary  data  of  which  are  the  elements  of  the 
celestial  movements ;  its  solution  depends  both  on  the  accuracy  of 
observations  and  on  the  perfection  of  analysis." 

LAPLACE,  Preface  to  the  Mecanique  "Celeste. 

228.  THE  solar  system,  as  it  was  known  at  the  beginning 
of  the  1 8th  century,  contained  18  recognised  members: 
the  sun,  six  planets,  ten  satellites  (one  belonging  to  the 
earth,  four  to  Jupiter,  and  five  to  Saturn),  and  Saturn's 
ring. 

Comets  were  known  to  have  come  on  many  occasions 
into  the  region  of  space  occupied  by  the  solar  system,  and 
there  were  reasons  to  believe  that  one  of  them  at  least 
(chapter  x.,  §  200)  was  a  regular  visitor ;  they  were,  how- 
ever, scarcely  regarded  as  belonging  to  the  solar  system, 
and  their  action  (if  any)  on  its  members  was  ignored,  a 
neglect  which  subsequent  investigation  has  completely 
justified.  Many  thousands  of  fixed  stars  had  also  been 
observed,  and  their  places  on  the  celestial  sphere  determined ; 
they  were  known  to  be  at  very  great  though  unknown 
distances  from  the  solar  system,  and  their  influence  on  it 
was  regarded  as  insensible. 

The  motions  of  the  1 8  members  of  the  solar  system  were 
tolerably  well  known ;  their  actual  distances  from  one 
another  had  been  roughly  estimated,  while  the  proportions 
between  most  of  the  distances  were  known  with  considerable 
accuracy.  Apart  from  the  entirely  anomalous  ring  of 
Saturn,  which  may  for  the  present  be  left  out  of  considera- 
tion, most  of  the  bodies  of  the  system  were  known  from 

287 


288  A  Short  History  of  Astronomy  [CH.  xi. 

observation  to  be  nearly  spherical  in  form,  and  the  rest  were 
generally  supposed  to  be  so  also. 

Newton  had  shewn,  with  a  considerable  degree  of  proba- 
bility, that  these  bodies  attracted  one  another  according  to 
the  law  of  gravitation ;  and  there  was  no  reason  to  suppose 
that  they  exerted  any  other  important  influence  on  one 
another's  motions.* 

The  problem  which  presented  itself,  and  which  may  con- 
veniently be  called  Newton's  problem,  was  therefore  : — 

Given  these  18  bodies,  and  their  positions  and  motions 
at  any  time,  to  deduce  from  their  mutual  gravitation  by 
a  process  of  mathematical  calculation  their  positions  and 
motions  at  any  other  time;  and  to  shew  that  these  agree 
with  those  actually  observed. 

Such  a  calculation  would  necessarily  involve,  among  other 
quantities,  the  masses  of  the  several  bodies  ;  it  was  evidently 
legitimate  to  assume  these  at  will  in  such  a  way  as  to  make 
the  results  of  calculation  agree  with  those  of  observation. 
If  this  were  done  successfully  the  masses  would  thereby  be 
determined.  In  the  same  way  the  commonly  accepted 
estimates  of  the  dimensions  of  the  solar  system  and  of  the 
shapes  of  its  members  might  be  modified  in  any  way  not 
actually  inconsistent  with  direct  observation. 

The  general  problem  thus  formulated  can  fortunately  be 
reduced  to  somewhat  simpler  ones. 

Newton  had  shewn  (chapter  ix.,  §  182)  that  an  ordinary 
sphere  attracted  other  bodies  and  was  attracted  by  them, 
as  if  its  mass  were  concentrated  at  its  centre  ;  and  that  the 
effects  of  deviation  from  a  spherical  form  became  very 
small  at  a  considerable  distance  from  the  body.  Hence, 
except  in  special  cases,  the  bodies  of  the  solar  system  could 
be  treated  as  spheres,  which  could  again  be  regarded  as 
concentrated  at  their  respective  centres.  It  will  be  con- 
venient for  the  sake  of  brevity  to  assume  for  the  future 
that  all  "  bodies "  referred  to  are  of  this  sort,  unless  the 
contrary  is  stated  or  implied.  The  effects  of  deviations 
from  spherical  form  could  then  be  treated  separately 

*  Some  other  influences  are  known — e.g.  the  sun's  heat  causes 
various  motions  of  our  air  and  water,  and  has  a  certain  minute  effect 
on  the  earth's  rate  of  rotation,  and  presumably  produces  similar 
effects  on  other  bodies. 


$  z 28]     Newtorfs  Problem  :  the  Problem  of  Three  Bodies    289 

when  required,  as  in  the  cases  of  precession  and  of 
other  motions  of  a  planet  or  satellite  about  its  centre,  and 
of  the  corresponding  action  of  a  non -spherical  planet  on  its 
satellites  ;  to  this  group  of  problems  belongs  also  that  of  the 
tides  and  other  cases  of  the  motion  of  parts  of  a  body  of 
any  form  relative  to  the  rest. 

Again,  the  solar  system  happens  to  be  so  constituted  that 
each  body's  motion  can  be  treated  as  determined  primarily 
by  one  other  body  only.  A  planet,  for  example,  moves 
nearly  as  if  no  other  body  but  the  sun  existed,  and  the 
moon's  motion  relative  to  the  earth  is  roughly  the  same  as 
if  the  other  bodies  of  the  solar  system  were  non-existent. 

The  problem  of  the  motion  of  two  mutually  gravitating 
spheres  was  completely  solved  by  Newton,  and  was 
shewn  to  lead  to  Kepler's  first  two  laws.  Hence  each 
body  of  the  solar  system  could  be  regarded  as  moving 
nearly  in  an  ellipse  round  some  one  body,  but  as  slightly 
disturbed  by  the  action  of  others.  Moreover,  by  a  general 
mathematical  principle  applicable  in  problems  of  motion, 
the  effect  of  a  number  of  small  disturbing  causes  acting 
conjointly  is  nearly  the  same  as  that  which  results  from 
adding  together  their  separate  effects.  Hence  each  body 
could,  without  great  error,  be  regarded  as  disturbed  by  one 
body  at  a  time;  the  several  disturbing  effects  could  then 
be  added  together,  and  a  fresh  calculation  could  be  made 
to  further  diminish  the  error.  The  kernel  of  Newton's 
problem  is  thus  seen  to  be  a  special  case  of  the  so-called 
problem  of  three  bodies,  viz.  :— 

Given  at  any  time  the  positions  and  motions  of  three 
i>iutually  gravitating  bodies ',  to  determine  their  positions  and 
motions  at  any  other  time. 

Even  this  apparently  simple  problem  in  its  general  form 
entirely  transcends  the  powers,  not  only  of  the  mathe- 
matical methods  of  the  early  i8th  century,  but  also  of 
those  that  have  been  devised  since.  Certain  special  cases 
have  been  solved,  so  that  it  has  been  shewn  to  be  possible 
to  suppose  three  bodies  initially  moving  in  such  a  way  that 
their  future  motion  can  be  completely  determined.  But 
these  cases  do  not  occur  in  nature. 

In  the  case  of  the  solar  system  the  problem  is  simplified, 
not  only  by  the  consideration  already  mentioned  that  one 

19 


290  A  Short  History  of  Astronomy  [CH.  xi. 

of  the  three  bodies  can  always  be  regarded  as  exercising 
only  a  small  influence  on  the  relative  motion  of  the  other 
two,  but  also  by  the  facts  that  the  orbits  of  the  planets 
and  satellites  do  not  differ  much  from  circles,  and  that 
the  planes  of  their  orbits  are  in  no  case  inclined  at  large 
angles  to  any  one  of  them,  such  as  the  ecliptic ;  in  other 
words,  that  the  eccentricities  and  inclinations  are  small 
quantities. 

Thus  simplified,  the  problem  has  been  found  to  admit 
of  solutions  of  considerable  accuracy  by  methods  of 
approximation.* 

In  the  case  of  the  system  formed  by  the  sun,  earth, 
and  moon,  the  characteristic  feature  is  the  great  distance 
of  the  sun,  which  is  the  disturbing  body,  fromxthe  other 
two  bodies  ;  in  the  case  of  the  sun  and  two  planets,  the 
enormous  mass  of  the  sun  as  compared  with  the  disturbing 
planet  is  the  important  factor.  Hence  the  methods  of 
treatment  suitable  for  the  two  cases  differ,  and  two  sub- 
stantially distinct  branches  of  the  subject,  lunar  theory  and 
planetary  theory,  have  developed.  The  problems  presented 
by  the  motions  of  the  satellites  of  Jupiter  and  Saturn,  though 
allied  to  those  of  the  lunar  theory,  differ  in  some  important 
respects,  and  are  usually  treated  separately. 

229.  As  we  have  seen,  Newton  made  a  number  of 
important  steps  towards  the  solution  of  his  problem,  but 
little  was  done  by  his  successors  in  his  own  country.  On 
the  Continent  also  progress  was  at  first  very  slow.  The 
Principia  was  read  and  admired  by  most  of  the  leading 
mathematicians  of  the  time,  but  its  principles  were  not 
accepted,  and  Cartesianism  remained  the  prevailing  philo- 
sophy. A  forward  step  is  marked  by  the  publication  by 
the  Paris  Academy  of  Sciences  in  1720  of  a  memoir  written 
by  the  Chevalier  de  Louville  (1671-1732)  on  the  basis  of 
Newton's  principles ;  ten  years  later  the  Academy  awarded 
a  prize  to  an  essay  on  the  planetary  motions  written  by 
John  Bernouilli  (1667-1748)  on  Cartesian  principles,  a 
Newtonian  essay  being  put  second.  In  1732  Maupertuis 
(chapter  x.,  §  221)  published  a  treatise  on  the  figure  of  the 

*  The  arithmetical  processes  of  working  out,  figure  by  figure,  a 
non-terminating  decimal  or  a  square  root  are  simple  cases  of  successive 
approximation. 


$$  229,  230]     Development  of  Gravitational  Astrono:ny         291 

earth  on  Newtonian  lines,  and  the  appearance  six  years  later 
of  Voltaire's  extremely  readable  Elements  de  la  Philosophic  de 
Newton  had  a  great  effect  in  popularising  the  new  ideas. 
The  last  official  recognition  of  Cartesianism  in  France 
seems  to  have  been  in  1740,  when  the  prize  offered  by  the 
Academy  for  an  essay  on  the  tides  was  shared  between 
a  Cartesian  and  three  eminent  Newtonians  (§  230).  — / 

The  rapid  development  of  gravitational  astronomy  that 
ensued  between  this  time  and  the  beginning  of  the 
1 9th  century  was  almost  entirely  the  work  of  five  great 
Continental  mathematicians,  Euler,  Clairaut,  D'Alembert, 
Lagrange,  and  Laplace,  of  whom  the  eldest  was  born  in 
1707  and  the  youngest  died  in  1827,  within  a  month  of  the 
centenary  of  Newton's  death.  Euler  was  a  Swiss,  Lagrange 
was  of  Italian  birth  but  French  by  extraction  and  to  a  great 
extent  by  adoption,  and  the  other  three  were  entirely 
French.  France  therefore  during  nearly  the  whole  of  the 
1 8th  century  reigned  supreme  in  gravitational  astronomy, 
and  has  not  lost  her  supremacy  even  to-day,  though  during 
the  present  century  America,  England,  Germany,  Italy,  and 
other  countries  have  all  made  substantial  contributions  to 
the  subject. 

It  is  convenient  to  consider  first  the  work  of  the  three 
first-named  astronomers,  and  to  treat  later  Lagrange  and 
Laplace,  who  carried  gravitational  astronomy  to  a  decidedly 
higher  stage  of  development  than  their  predecessors. 

230.  Leonhard  Euler  was  born  at  Basle  in  1707,  14  years 
later  than  Bradley  and  six  years  earlier  than  Lacaille.  He 
was  the  son  of  a  Protestant  minister  who  had  studied 
mathematics  undery^;^^  Bernouilli  (1654-1 705),  the  first  of 
a  famous  family  of  mathematicians.  Leonhard  Euler  him- 
self was  a  favourite  pupil  of  John  Bernouilli  (the  younger 
brother  of  James),  and  was  an  intimate  friend  of  his  two 
sons,  one  of  whom,  Daniel  (1700-1782),  was  not  only  a  dis- 
tinguished mathematician  like  his  father  and  uncle,  but  was 
also  the  first  important  Newtonian  outside  Great  Britain. 
Like  so  many  other  astronomers,  Euler  began  by  studying 
theology,  but  was  induced  both  by  his  natural  tastes  and 
by  the  influence  of  the  Bernouillis  to  turn  his  attention  to 
mathematics.  Through  the  influence  of  Daniel  Bernouilli, 
who  had  recently  been  appointed  to  a  professorship  at 


292  A  Short  History  of  Astronomy  [CH.  XI. 

St.  Petersburg,  Euler  received  and  accepted  an  invitation 
to  join  the  newly  created  Academy  of  Sciences  there  (1727). 
This  first  appointment  carried  with  it  a  stipend,  and  the 
duties  were  the  general  promotion  of  science ;  subsequently 
Euler  undertook  more  definite  professorial  work,  but  most 
of  his  energy  during  the  whole  of  his  career  was 
devoted  to  writing  mathematical  papers,  the  majority  of 
which  were  published  by  the  St.  Petersburg  Academy. 
Though  he  took  no  part  in  politics,  Russian  autocracy 
appears  to  have  been  oppressive  to  him,  reared  as  he  had 
been  among  Swiss  and  Protestant  surroundings ;  and  in 
1741  he  accepted  an  invitation  from  Frederick  the  Great, 
a  despot  of  a  less  pronounced  type,  to  come  to  Berlin,  and 
assist  in  reorganising  the  Academy  of  Sciences  there.  On 
being  reproached  one  day  by  the  Queen  for  his  taciturn 
and  melancholy  demeanour,  he  justified  his  silence  on  the 
ground  that  he  had  just -come  from  a  country  where  speech 
was  liable  to  lead  to  hanging  ;  *  but  notwithstanding  this 
frank  criticism  he  remained  on  good  terms  with  the  Russian 
court,  and  continued  to  draw  his  stipend  as  a  member 
of  the  St.  Petersburg  Academy  and  to  contribute  to  its 
Transactions.  Moreover,  after  25  years  spent  at  Berlin,  he 
accepted  a  pressing  invitation  from  the  Empress  Catherine  II. 
and  returned  to  Russia  (1766). 

He  had  lost  the  use  of  one  eye  in  1735,  a  disaster  which 
called  from  him  the  remark  that  he  would  henceforward 
have  less  to  distract  him  from  his  mathematics ;  the  second 
eye  went  soon  after  his  return  to  Russia,  and  with  the 
exception  of  a  short  time  during  which  an  operation  restored 
the  partial  use  of  one  eye  he  remained  blind  till  the  end 
of  his  life.  But  this  disability  made  little  .difference  to  his 
astounding  scientific  activity  ;  and  it  was  only  after  nearly 
17  years  of  blindness  that  as  a  result  of  a  fit  of  apoplexy 
"he  ceased  to  live  and  to  calculate"  (1783). 

Euler  was  probably  the  most  versatile  as  well  as  the  most 
prolific  of  mathematicians  of  all  time.  There  is  scarcely 
any  branch  of  modern  analysis  to  which  he  was  not  a  large 
contributor,  and  his  extraordinary  powers  of  devising  and 
applying  methods  of  calculation  were  employed  by  him 
with  great  success  in  each  of  the  existing  branches  of  applied 

*  "C'est  que  je  viens  d'un  pays  oil,  quand  on  parle,  on  est  pendu," 


$  23i]  Euler  and  Clairaut  293 

mathematics ;  problems  of  abstract  dynamics,  of  optics,  of 
the  motion  of  fluids,  and  of  astronomy  were  all  in  turn 
subjected  to  his  analysis  and  solved.  The  extent  of  his 
writings  is.  shewn  by  the  fact  that,  in  addition  to  several 
books,  he  wrote  about  800  papers  on  mathematical  and 
physical  subjects ;  it  is  estimated  that  a  complete  edition 
of  his  works  would  occupy  25  quarto  volumes  of  about 
600  pages  each. 

Euler's  first  contribution  to  astronomy  was  an  essay  on 
the  tides  which  obtained  a  share  of  the  Academy  prize  for 
1740  already  referred  to,  Daniel  Bernouilli  and  Maclaurin 
(chapter  x.,  §  196)  being  the  other  two  Newtonians.  The 
problem  of  the  tides  was,  however,  by  no  means  solved  by 
any  of  the  three  writers. 

He  gave  two  distinct  solutions  of  the  problem  of  three 
bodies  in  a  form  suitable  for  the  lunar  theory,  and  made 
a  number  of  extremely  important  and  suggestive  though 
incomplete  contributions  to  planetary  theory.  In  both 
subjects  his  work  was  so  closely  connected  with  that  of 
Glairaut  and  D'Alembert  that  it  is  more  convenient  to 
discuss  it  in  connection  with  theirs. 

231.  Alexis  Claude  Clairaut,  born  at  Paris  in  1713, 
belongs  to  the  class  of  precocious  geniuses.  He  read  the 
Infinitesimal  Calculus  and  Conic  Sections  at  the  age  of  ten, 
presented  a  scientific  memoir  to  the  Academy  of  Sciences 
before  he  was  13,  and  published  a  book  containing  some 
important  contributions  to  geometry  when  he  was  18, 
thereby  winning  his  admission  to  the  Academy. 

Shortly  afterwards  he  took  part  in  Maupertuis'  expedition 
to  Lapland  (chapter  x.,  §  221),  and  after  publishing  several 
papers  of  minor  importance  produced  in  1743  his  classical 
work  on  the  figure  of  the  earth.  In  this  he  discussed  in 
a  far  more  complete  form  than  either  Newton  or  Maclaurin 
the  form  which  a  rotating  body  like  the  earth  assumes 
under  the  influence  of  the  mutual  gravitation  of  its  parts, 
certain  hypotheses  of  a  very  general  nature  being  made  as 
to  the  variations  of  density  in  the  interior ;  and  deduced 
formulae  for  the  changes  in  different  latitudes  of  the  accelera- 
tion due  to  gravity,  which  are  in  satisfactory  agreement  with 
the  results  of  pendulum  experiment. 

Although  the  subject  has  since  been  more  elaborately 


294  d  Short  History  of  Astronomy  [Cn.  XI. 

and  more  generally  treated  by  later  writers,  and  a  good 
many  additions  have  been  made,  few  if  any  results  of 
fundamental  importance  have  been  added  to  those  con- 
tained in  Clairaut's  book. 

He  next  turned  his  attention  to  the  problem  of  three 
bodies,  obtained  a  solution  suitable  for  the  moon,  and  made 
some  progress  in  planetary  theory. 

Halley's  comet   (chapter   x.,  §200)  was  "due"   about 


\ 


FIG.  80.— The  path  of  Halley's  comet. 

1758;  as  the  time  approached  Clairaut  took  up  the  task 
of  computing  the  perturbations  which  it  would  probably  have 
experienced  since  its  last  appearance,  owing  to  the  influence 
of  the  two  great  planets,  Jupiter  and  Saturn,  close  to  both 
of  which  it  would  have  passed.  An  extremely  laborious 
calculation  shewed  that  the  comet  would  have  been  retarded 
about  100  days  by  Saturn  and  about  518  days  by  Jupiter, 
and  he  accordingly  announced  to  the  Academy  towards  the 
end  of  1758  that  the  comet  might  be  expected  to  pass  its 


$  232]  Ha  I  ley's  Comet :  D'Akmbert  295 

perihelion  (the  point  of  its  orbit  nearest  the  sun,  p  in  fig.  80) 
about  April  i3th  of  the  following  year,  though  owing  to 
various  defects  in  his  calculation  there  might  be  an  error  of 
a  month  either  way.  The  comet  was  anxiously  watched  for 
by  the  astronomical  world,  and  was  actually  discovered  by 
an  amateur,  George  Palitzsch  (1723-1788)  of  Saxony,  on 
Christmas  Day,  1758  ;  it  passed  its  perihelion  just  a  month 
and  a  day  before  the  time  assigned  by  Clairaut. 

Halley's  brilliant  conjecture  was  thus  justified  ;  a  new 
member  was  added  to  the  solar  system,  and  hopes  were 
raised — to  be  afterwards  amply  fulfilled — that  in  other 
cases  also  the  motions  of  comets  might  be  reduced  to 
rule,  and  calculated  according  to  the  same  principles  as 
those  of  less  erratic  bodies.  The  superstitions  attached 
to  comets  were  of  course  at  the  same  time  still  further 
shaken. 

Clairaut  appears  to  have  had  great  personal  charm  and 
to  have  been  a  conspicuous  figure  in  Paris  society.  Un- 
fortunately his  strength  was  not  equal  to  the  combined 
claims  of  social  and  scientific  labours,  and  he  died  in  1765 
at  an  age  when  much  might  still  have  been  hoped  from  his 
extraordinary  abilities.* 

232.  Jean-le-Rond  D'Akmbert  was  found  in  1717  as  an 
infant  on  the  steps  of  the  church  of  St.  Jean-le-Rond  in 
Paris,  but  was  afterwards  recognised,  and  to  some  extent 
provided  for,  by  his  father,  though  his  home  was  with  his 
foster  parents.  After  receiving  a  fair  school  education, 
he  studied  law  and  medicine,  but  then  turned  his  attention 
to  mathematics.  He  first  attracted  notice  in  mathematical 
circles  by  a  paper  written  in  1738,  and  was  admitted  to 
the  Academy  of  Sciences  two  years  afterwards.  His  earliest 
important  work  was  the  Traite  de  Dynamique  (1743),  whic  i 
contained,  among  other  contributions  to  the  subject,  the 
first  statement  of  a  dynamical  principle  which  bears  his 
name,  and  which,  though  in  one  sense  only  a  corollary 
from  Newton's  Third  Law  of  Motion,  has  proved  to  be  of 
immense  service  in  nearly  all  general  dynamical  problems, 

*  Longevity  has  been  a  remarkable  characteristic  of  the  great 
mathematical  astronomers:  Newton  died  in  his  85th  year;  Euler, 
Lagrange,  and  Laplace  lived  to  be  more  than  75,  and  D'Alembert 
was  almost  66  at  his  death. 


296  A  Short  History  of  Astronomy  ten.  xi. 

astronomical  or  otherwise.  During  the  next  few  years  he 
made  a  number  of  contributions  to  mathematical  physics, 
as  well  as  to  the  problem  of  three  bodies ;  and  published 
in  1749  his  work  on  precession  and  nutation,  already 
referred  to  (chapter  x.,  §  215).  From  this  time  onwards 
he  began  to  give  an  increasing  part  of  his  energies  to  work 
outside  mathematics.  For  some  years  he  collaborated 
with  Diderot  in  producing  the  famous  French  Encyclopaedia, 
which  began  to  appear  in  1751,  and  exercised  so  great 
an  influence  on  contemporary  political  and  philosophic 
thought.  D'Alembert  wrote  the  introduction,  which  was 
read  to  the  Academic  Franfaise*  in  1754  on  the  occasion 
of  his  admission  to  that  distinguished  body,  as  well  as  a 
variety  of  scientific  and  other  articles.  In  the  later  part 
of  his  life,  which  ended  in  1783,  he  wrote  little  on  mathe- 
matics, but  published  a  number  of  books  on  philosophical, 
literary,  and  political  subjects ;  t  as  secretary  of  the 
Academy  he  also  wrote  obituary  notices  (eloges)  of  some 
70  of  its  members.  He  was  thus,  in  Carlyle's  words,  "  of 
great  faculty,  especially  of  great  clearness  and  method ; 
famous  in  Mathematics  ;  no  less  so,  to  the  wonder  of  some, 
in  the  intellectual  provinces  of  Literature." 

D'Alembert  and  Clairaut  were  great  rivals,  and  almost 
every  work  of  the  latter  was  severely  criticised  by  the 
former,  while  Clairaut  retaliated  though  with  much  less 
zeal  and  vehemence.  The  great  popular  reputation  acquired 
by  Clairaut  through  his  work  on  Halley's  comet  appears 
to  have  particularly  excited  D'Alembert's  jealousy.  The 
rivalry,  though  not  a  pleasant  spectacle,  was,  however,  use- 
ful in  leading  to  the  detection  and  subsequent  improvement 
of  various  weak  points  in  the  work  of  each.  In  other 
respects  D'Alembert's  personal  characteristics  appear  to 
have  been  extremely  pleasant.  He  was  always  a  poor 
man,  but  nevertheless  declined  magnificent  offers  made  to 
him  by  both  Catherine  II.  of  Russia  and  Frederick  the 

*  This  body,  which  is  primarily  literary,  has  to  be  distinguished 
from  the  much  less  famous  Paris  Academy  of  Sciences,  constantly 
referred  to  (often  simply  as  the  Academy)  in  this  chapter  and  the 
preceding. 

,  f  E.g.    Melanges  de  Philosophic,    de   FHistoire,    et  de    Litle'ra'ure ; 
Elements  de  Philosophic ;  Sur  la  Destruction  des  Je'suites. 


$  233]  D'Alembert :  Lunar  Theory  297 

Great  of  Prussia,  and  preferred  to  keep  his  independence, 
though  he  retained  the  friendship  of  both  sovereigns  and 
accepted  a  small  pension  from  the  latter.  He  lived  ex- 
tremely simply,  and  notwithstanding  his  poverty  was  very 
generous  to  his  foster-mother,  to  various  young  students, 
and  to  many  others  with  whom  he  came  into  contact. 

233.  Euler,  Clairaut,  and  D'Alembert  all  succeeded  in 
obtaining  independently  and  nearly  simultaneously  solutions 
of  the  problem  of  three  bodies  in  a  form  suitable  for  lunar 
theory.  Euler  published  in  1746  some  rather  imperfect 
Tables  of  the  Moon,  which  shewed  that  he  must  have 
already  obtained  his  solution.  Both  Clairaut  and  D'Alembert 
presented  to  the  Academy  in  1747  memoirs  containing 
their  respective  solutions,  with  applications  to  the  moon 
as  well  as  to  some  planetary  problems.  In  each  of  these 
memoirs  occurred  the  same  difficulty  which  Newton  had 
met  with  :  the  calculated  motion  of  the  moon's  apogee  was 
only  about  half  the  observed  result.  Clairaut  at  first  met 
this  difficulty  by  assuming  an  alteration  in  the  law  of  gravi- 
tation, and  got  a  result  which  seemed  to  him  satisfactory 
by  assuming  gravitation  to  vary  partly  as  the  inverse  square 
and  partly  as  the  inverse  cube  of  the  distance.*  Euler  also 
had  doubts  as  to  the  correctness  of  the  inverse  square. 
Two  years  later,  however  (1749),  on  going  through  his 
original  calculation  again,  Clairaut  discovered  that  certain 
terms,  which  had  appeared  unimportant  at  the  beginning  of 
the  calculation  and  had  therefore  been  omitted,  became 
important  later  on.  When  these  were  taken  into  account, 
the  motion  of  the  apogee  as  deduced  from  theory  agreed 
very  nearly  with  that  observed.  This  was  the  first  of  several 
cases  in  which  a  serious  discrepancy  between  theory  and 
observation  has  at  first  discredited  the  law  of  gravitation, 
but  has  subsequently  been  explained  away,  and  has  thereby 
given  a  new  verification  of  its  accuracy.  When  Clairaut 
had  announced  his  discovery,  Euler  arrived  by  a  fresh 
calculation  at  substantially  the  same  result,  while  D'Alembert 
by  carrying  the  approximation  further  obtained  one  that 
was  slightly  more  accurate.  A  fresh  calculation  of  the 
motion  of  the  moon  by  Clairaut  won  the  prize  on  the 
subject  offered  by  the  St.  Petersburg  Academy,  and  was 

*  I.e.  he  assumed  a  law  of  attraction  represented  by  yu/r2  +  v\i*. 


298  A  Short  History  of  Astronomy  [CH.  XI. 

published  in  1752,  with  the  title  TLeorie  de  la  Lune.  Two 
years  later  he  published  a  set  of  lunar  tables,  and  just  before 
his  death  (1765)  he  brought  out  a  revised  edition  of  the 
Theorie  de  la  Lune  in  which  he  embodied  a  new  set  of 
tables. 

D'Alembert  followed  his  paper  of  1747  by  a  complete 
lunar  theory  (with  a  moderately  good  set  of  tables),  which, 
though  substantially  finished  in  1751,  was  only  published 
in  1754  as  the  first  volume  of  his  Recherches  sur  differens 
points  important  du  systeme  du  Monde.  In  1756  he  pub- 
lished an  improved  set  cf  tables,  and  a  few  months  afterward 
a  third  volume  of  Recherches  with  some  fresh  developments 
of  the  theory.  The  second  volume  of  his  Opuscules 
Mathematiques  (1762)  contained  another  memoir  on  the 
subject  with  a  third  set  of  tables,  which  were  a  slight 
improvement  on  the  earlier  ones. 

Euler's  first  lunar  theory  (Theoria  Motuum  Lunae)  was 
published  in  1753,  though  it  had  been  sent  to  the  St. 
Petersburg  Academy  a  year  or  two  earlier.  In  an  appendix  * 
he  points  out  with  characteristic  frankness  the  defects  from 
which  his  treatment  seems  to  him  to  suffer,  and  suggests 
a  new  method  of  dealing  with  the  subject.  It  was  on  this 
theory  that  Tobias  Mayer  based  his  tables,  referred  to  in 
the  preceding  chapter  (§226).  Many  years  later  Euler 
devised  an  entirely  new  way  of  attacking  the  subject,  and 
after  some  preliminary  papers  dealing  generally  with  the 
method  and  with  special  parts  of  the  problem,  he  worked 
out  the  lunar  theory  in  great  detail,  with  the  help  of  one 
of  his  sons  and  two  other  assistants,  and  published  the 
whole,  together  with  tables,  in  1772.  He  attempted,  but 
without  success,  to  deal  in  this  theory  with  the  secular 
acceleration  of  the  mean  motion  which  Halley  had  detected 
(chapter  x.,  §  201). 

In  any  mathematical  treatment  of  an  astronomical  problem 
some  data  have  to  be  borrowed  from  observation,  and  of 
the  three  astronomers  Clairaut  seems  to  have  been  the  most 
skilful  in  utilising  observations,  many  of  which  he  obtained 
from  Lacaille.  Hence  his  tables  represented  the  actual 

*  This  appendix  is  memorable  as  giving  for  the  first  time  the 
method  of  variation  of  parameters  which  Lagrange  afterwards 
developed  and  used  with  such  success. 


$$  234,  235]  Lunar  Theory  299 

motions  of  the  moon  far  more  accurately  than  those  of 
D'Alembert,  and  were  even  superior  in  some  points  to  those 
based  on  Euler's  very  much  more  elaborate  second  theory ; 
Clairaut's  last  tables  were  seldom  in  error  more  than  i|', 
and  would  hence  serve  to  determine  the  longitude  to 
within  about  |°.  Clairaut's  tables  were,  however,  never 
much  used,  since  Tobias  Mayer's  as  improved  by 
Bradley  were  found  in  practice  to  be  a  good  deal  more 
accurate  ;  but  Mayer  borrowed  so  extensively  from  observa- 
tion that  his  formulae  cannot  be  regarded  as  true  deductions 
from  gravitation  in  the  same  sense  in  which  Clairaut's  were. 
Mathematically  Euler's  second  (theory  is  the  most  interest- 
ing and  was  of  the  greatest  importance  as  a  basis  for  later 
developments.  The  most  modern  lunar  theory  *  is  in 
some  sense  a  return  to  Euler's  methods. 

234.  Newton's  lunar  theory  may  be  said  to  have  given  a 
qualitative  account  of  the  lunar  inequalities  known  by 
observation  at  the  time  when  the  Principia  was  published, 
and  to  have  indicated  others  which  had  not  yet  been 
observed.  But  his  attempts  to  explain  these  irregularities 
quantitatively  were  only  partially  successful. 
lEuler,  Clairaut,  and  D'Alembejt  threw  the  lunar  theory 
into  an  entirely  new  form  by  using  analytical  methods 
instead  of  geometrical ;  one  advantage  of  this  was  that  by 
the  expenditure  of  the  necessary  labour  calculations  could 
in  general  be  carried  further  when  required  and  lead  to  a 
higher  degree  of  accuracy.  The  result  of  their  more 
elaborate  development  was  that — with  one  exception — the 
inequalities  known  from  observation  were  explained  with  a 
considerable  degree  of  accuracy  quantitatively  as  well  as 
qualitatively  ;  and  thus  tables,  such  as  those  of  Clairaut, 
based  on  theory,  represented  the  lunar' motions  very  closely. 
'Fhe  one  exception  was  the  secular—  acceleration  :  we  have 
just  seen  that  Euler  failed  to  explain  it ;  D'Alembert  was 
equally  unsuccessful,  and  Clairaut  does  not  appear  to  have 
considered  the  question. 

2*35.  The  chief  inequalities  in  planetary  motion  which 
observation  had  revealed  up  to  Newton's  time  were  the 
forward  motion  of  the  apses  of  the  earth's  orbit  and  a  very 

*  That  of  the  distinguished  American  astronomer  Dr.  G.  W.  Hill 
(chapter  xin.,  §  286). 

4~— ' 

u-«.^-^< 


300  A  Short  History  of  Astronomy  [CH.  XI. 

slow  diminution  in  the  obliquity  of  the  ecliptic.  To  these 
may  be  added  the  alterations  in  the  rates  of  motion  of 
Jupiter  and  Saturn  discovered  by  Halley  (chapter  x.,  §  204). 

Newton  had  shewn  generally  that  the  perturbing  effect  of 
another  planet  would  cause  displacements  in  the  apses 
of  any  planetary  orbit,  and  an  alteration  in  the  relative 
positions  of  the  planes  in  which  the  disturbing  and  disturbed 
planet  moved ;  but  he  had  made  no  detailed  calculations, 
Some  effects  of  this  general  nature,  in  addition  to  those 
already  known,  were,  however,  indicated  with  more  or  less 
distinctness  as  the  result  of  observation  in  various  planetary 
tables  published  between  the  date  of  the  Principia  and  the 
middle  of  the  i8th  century. 

The  irregularities  in  the  motion  of  the  earth,  shewing 
themselves  as  irregularities  in  the  apparent  motion  of  the 
sun,  and  those  of  Jupiter  and  Saturn,  were  the  most 
interesting  and  important  of  the  planetary  inequalities,  and 
prizes  for  essays  on  one  or  another  subject  were  offered 
several  times  by  the  Paris  Academy. 

i^h^_pei±urbations  of  the  ™nnn  nprpggqrily  invqlved — by 
the  principle  of  action  and  reaction— corresponding  though 
smaller  perTurbations  of  the  earth  ;  these  were_f)igrnggprl  on 
various  occasions  by  Clairaut  and  Euler,  and  still  more 
fully  by  D'AlemrJeTtT"^ 

In  Clairaut's  paper  of  1747  (§  233)  he  made  some 
attempt  to  apply  his  solution  of  the  problem  of  three  bodies 
to  the  case  of  the  sun,  earth,  and  Saturn,  which  on  account 
of  Saturn's  great  distance  from  the  sun  (nearly  ten  times 
that  of  the  earth)  is  the  planetary  case  most  like  that  of  the 
earth,  moon,  and  sun  (cf.  §  228). 

Ten  years  later  he  discussed  in  some  detail  the  perturba- 
tions of  the  earth  due  to  Venus  and  to  the  moon.  This 
paper  was  remarkable  as  containing  the  first  attempt  to 
estimate  masses  of  celestial  bodies  by  observation  of  per- 
turbations due  to  them.  Clairaut  applied  this  method  to 
the  moon  and  to  Venus,  by  calculating  perturbations  in 
the  earth's  motion  due  to  their  action  (which  necessarily 
depended  on  their  masses),  and  then  comparing  the  results 
with  Lacaille's  observations  of  the  sun.  The  mass  of  the 
moon  was  thus  found  to  be  about  ^T  and  that  of  Venus 
f  that  of  the  earth ;  the  first  result  was  a  considerable 


§  236]  Planetary  Theory  301 

improvement  on  Newton's  estimate  from  tides  (chapter  ix., 
§  189),  and  the  second,  which  was  entirely  new,  previous 
estimates  having  been  merely  conjectural,  is  in  tolerable 
agreement  with  modern  measurements.*  It  is  worth 
noticing  as  a  good  illustration  of  the  reciprocal  influence 
of  observation  and  mathematical  theory  that,  while  Clairaut 
used  Lacaille's  observations  for  his  theory,  Lacaille  in  turn 
used  Clairaut's  calculations  of  the  perturbations  of  the 
earth  to  improve  his  tables  of  the  sun  published  in  1758. 

Clairaut's  method  of  solving  the  problem  of  three  bodies 
was  also  applied  by  Joseph  Jerome  Le  Francois  Lalande 
(1732-1807),  who  is  chiefly  known  as  an  admirable  popu- 
lariser  of  astronomy  but  was  also  an  indefatigable  calculator 
and  observer,  to  the  perturbations  of  Mars  by  Jupiter,  of 
Venus  by  the  earth,  and  of  the  earth  by  Mars,  but  with 
only  moderate  success. 

D'Alembert  made  some  progress  with  the  general  treat- 
ment of  planetary  perturbations  in  the  second  volume  of 
his  Recherches,  and  applied  his  methods  to  Jupiter  and 
Saturn. 

236.  Euler  carried  the  general  theory  a  good  deal  further 
in  a  series  of  papers  beginning  in  1747.  He  made  several 
attempts  to  explain  the  irregularities  of  Jupiter  and  Saturn, 
but  never  succeeded  in  representing  the  observations  satis- 
factorily. He  shewed,  however,  that  the  perturbations  due  to 
the  other  planets  would  cause  the  earth's  apse  line  to  advance 
about  13"  annually,  and  the  obliquity  of  the  ecliptic  to 
diminish  by  about  48"  annually,  both  results  being  in  fair 
accordance  both  with  observations  and  with  more  elaborate 
calculations  made  subsequently.  He  indicated  also  the 
existence  of  various  other  planetary  irregularities,  which  for 
the  most  part  had  not  previously  been  observed. 

In  an  essay  to  which  the  Academy  awarded  a  prize 
in  1756,  but  which  was  first  published  in  1771,  he  developed 
with  some  completeness  a  method  of  dealing  with  per- 
turbations which  he  had  indicated  in  his  lunar  theory 
of- 1 753.  As  this  method,  known  as  that  of  the  variation 
of  the  elements  or  parameters,  played  a  very  important  part 

*  They  give  about  78  for  the  mass  of  Venus  compared  to  that  of 
the  earth. 


302  A  Short  History  of  Astronomy  [CH.  XF. 

in  subsequent  researches,  it  may  be  worth  while  to  attempt 
to  give  a  sketch  of  it. 

If  perturbations  are  ignored,  a  planet  can  be  regarded  as 
moving  in  an  ellipse  with  the  sun  in  one  focus.  The  size  and 
shape  of  the  ellipse  can  be  defined  by  the  length  of  its  axis 
and  by  the  eccentricity  ;  the  plane  in  which  the  ellipse  is 
situated  is  determined  by  the  position  of  the  line,  called  the 
line  of  nodes,  in  which  it  cuts  a  fixed  plane,  usually  taken 
to  be  the  ecliptic,  and  by  the  inclination  of  the  two  planes. 
When  these  four  quantities  are  fixed,  the  ellipse  may  still 
turn  about  its  focus  in  its  own  plane,  but  if  the  direction 
of  the  apse  line  is  also  fixed  the  ellipse  is  completely 
determined.  If,  further,  the  position  of  the  planet  in  its 
ellipse  at  any  one  time  is  known,  the  motion  is  completely 
determined  and  its  position  at  any  other  time  can  be 
calculated.  There  are  thus  six  quantities  known  as  elements 
which  completely  determine  the  motion  of  a  planet  not 
subject  to  perturbation. 

When  perturbations  are  taken  into  account,  the  path 
described  by  a  planet  in  any  one  revolution  is  no  longer 
an  ellipse,  though  it  differs  very  slightly  from  one ;  while  in 
the  case  of  the  moon  the  deviations  are  a  good  deal  greater. 
But  if  the  motions  of  a  planet  at  two  widely  different 
epochs  are  compared,  though  on  each  occasion  the  path 
described  is  very  nearly  an  ellipse,  the  ellipses  differ  in 
some  respects.  For  example,  between  the  time  of  Ptolemy 
(A.D.  150)  and  that  of  Euler  the  direction  of  the  apse  line 
of  the  earth's  orbit  altered  by  about  5°,  and  some  of  the 
other  elements  also  varied  slightly.  Hence  in  dealing  with 
the  motion  of  a  planet  through  a  long  period  of  time  it  is 
convenient  to  introduce  the  idea  of  an  elliptic  path  which 
is  gradually  changing  its  position  and  possibly  also  its  size 
and  shape.  One  consequence  is  that  the  actual  path 
described  in  the  course  of  a  considerable  number  of 
revolutions  is  a  curve  no  longer  bearing  much  resemblance 
to  an  ellipse.  If,  for  example,  the  apse  line  turns  round 
uniformly  while  the  other  elements  remain  unchanged,  the 
path  described  is  like  that  shewn  in  the  figure. 

Euler  extended  this  idea  so  as  to  represent  any  per- 
turbation of  a  planet,  whether  experienced  in  the  course 
of  one  revolution  or  in  a  longer  time,  by  means  of  changes 


$  236)  Variation  of  the  Elements  303 

in  an  elliptic  orbit.  For  wherever  a  planet  may  be  and 
whatever  (within  certain  limits  *)  be  its  speed  or  direction 
of  motion  some  ellipse  can  be  found,  having  the  sun  in 
one  focus,  such  that  the  planet  can  be  regarded  as  moving 
in  it  for  a  short  time.  Hence  as  the  planet  describes  a 
perturbed  orbit  it  can  be  regarded  as  moving  at  any  instant 


FIG.  81. — A  varying  ellipse. 

in  an  ellipse,  which,  however,  is  continually  altering  its 
position  or  other  characteristics.  Thus  the  problem  of 
discussing  the  planet's  motion  becomes  that  of  determining 
the  elements  of  the  ellipse  which  represents  its  motion  at 
any  time.  Euler  shewed  further  how,  when  the  position 
of  the  perturbing  planet  was  known,  the  corresponding 

*  The  orbit  might  be  a  parabola  or  hyperbola,  though  this  does 
not  occur  in  the  case  of  any  known  planet. 


304  A  Short  History  of  Astronomy  [CH.  3.1. 

rates  of  change  of  the  elements  of  the  varying  ellipse 
could  be  calculated,  and  made  some  progress  towards 
deducing  from  these  data  the  actual  elements ;  but  he 
found  the  mathematical  difficulties  too  great  to  be  over- 
come except  in  some  of  the  simpler  cases,  and  it  was 
reserved  for  the  next  generation  of  mathematicians,  notably 
Lagrange,  to  shew  the  full  power  of  the  method. 

237.  Joseph  Louis  Lagrange  was  born  at  Turin  in  1736, 
when  Clairaut  was  just  starting  for  Lapland  and  D'Alembert 
was  still  a  child ;  he  was  descended  from  a  French  family 
three  generations  of  which  had  lived  in  Italy.  He  shewed 
extraordinary  mathematical  talent,  and  when  still  a  mere 
boy  was  appointed  professor  at  the  Artillery  School  of  his 
native  town,  his  pupils  being  older  than  himself.  A  few 
years  afterwards  he  was  the  chief  mover  in  the  foundation 
of  a  scientific  society,  afterwards  the  Turin  Academy  of 
Sciences,  which  published  in  1759  its  first  volume  of 
Transactions,  containing  several  mathematical  articles  by 
Lagrange,  which  had  been  written  during  the  last  few 
years.  One  of  these  *  so  impressed  Euler,  who  had  made 
a  special  study  of  the  subject  dealt  with,  that  he  at  once 
obtained  for  Lagrange  the  honour  of  admission  to  the 
Berlin  Academy. 

In  1764  Lagrange  won  the  prize  offered  by  the  Paris 
Academy  for  an  essay  on  the  libration  of  the  moon.  In 
this  essay  he  not  only  gave  the  first  satisfactory,  though 
still  incomplete,  discussion  of  the  librations  (chapter  vi., 
§  133)  of  the  moon  due  to  the  non-spherical  forms  of  both 
the  earth  and  moon,  but  also  introduced  an  extremely 
general  method  of  treating  dynamical  problems,!  which 
is  the  basis  of  nearly  all  the  higher  branches  of  dynamics 
which  have  been  developed  up  to  the  present  day. 

Two  years  later  (1766)  Frederick  II.,  at  the  suggestion 
of  D'Alembert,  asked  Lagrange  to  succeed  Euler  (who 
had  just  returned  to  St.  Petersburg)  as  the  head  of  the 
mathematical  section  of  the  Berlin  Academy,  giving  as  a 
reason  that  the  greatest  king  in  Europe  wished  to  have 
the  greatest  mathematician  in  Europe  at  his  court. 

*   On  the  Calculus  of  Variations. 

f  The  establishment  of  the  general  equations  of  motion  by 
a  combination  of  virtual  velocities  and  U  Alemberf  s  principle. 


LAGRANGE. 


[  To  face  p.  305. 


§  237l  Life  of  Lagrange  305 

Lagrange  accepted  this  magnificently  expressed  invitation 
and  spent  the  next  21  years  at  Berlin. 

During  this  period  he  produced  an  extraordinary  series 
of  papers  on  astronomy,  on  general  dynamics,  and  on  a 
variety  of  subjects  in  pure  mathematics.  Several  of  the 
most  important  of  the  astronomical  papers  were  sent  to 
Paris  and  obtained  prizes  offered  by  the  Academy  ;  most 
of  the  other  papers — about  60  in  all — were  published  by 
the  Berlin  Academy.  During  this  period  he  wrote  also 
his  great  Mecanique  Analytique,  one  of  the  most  beautiful 
of  all  mathematical  books,  in  which  he  developed  fully 
the  general  dynamical  ideas  contained  in  the  earlier  paper 
on  libration.  Curiously  enough  he  had  great  difficulty  in 
finding  a  publisher  for  his  masterpiece,  and  it  only  appeared 
in  1788  in  Paris.  A  year  earlier  he  had  left  Berlin  in 
consequence  of  the  death  of  Frederick,,  and  accepted  an 
invitation  from  Louis  XVI.  to  join  the  Paris  Academy. 
About  this  time  he  suffered  from  one  of  the  fits  of  melan- 
choly with  which  he  was  periodically  seized  and  which  are 
generally  supposed  to  have  been  due  to  overwork  during 
his  career  at  Turin.  It  is  said  that  he  never  looked  at 
the  Mecanique  Analytique  for  two  years  after  its  publication, 
and  spent  most  of  the  time  over  chemistry  and  other 
branches  of  natural  science  as  well  as  in  non-scientific 
pursuits.  In  1790  he  was  made  president  of  the  Com- 
mission appointed  to  draw  up  a  new  system  of  weights 
and  measures,  which  resulted  in  the  establishment  of  the 
metric  system  ;  and  the  scientific  work  connected  with  this 
undertaking  gradually  restored  his  interest  in  mathematics 
and  astronomy.  He  always  avoided  politics,  and  passed 
through  the  Revolution  uninjured,  unlike  his  friend 
Lavoisier  the  great  chemist  and  Bailly  the  historian  of 
astronomy,  both  of  whom  were  guillotined  during  the  Terror. 
He  was  in  fact  held  in  great  honour  by  the  various  govern- 
ments which  ruled  France  up  to  the  time  of  his  death  ; 
in  1793  he  was  specially  exempted  from  a  decree  of  banish- 
ment directed  against  all  foreigners;  subsequently  he  was 
made  professor  of  mathematics,  first  at  the  Ecole  Normale 
(1795),  and  then  at  the  £cole  Polytechnique  (1797),  the 
last  appointment  being  retained  till  his  death  in  1813. 
During  this  period  of  his  life  he  published,  in  addition 

20 


306  A  Short  History  of  Astronomy  [CH.  XL 

to  a  large  number  of  papers  on  astronomy  and  mathematics, 
three  important  books  on  pure  mathematics,*  and  at  the 
time  of  his  death  had  not  quite  finished  a  second  edition 
of  the  Mecanique  Analytique,  the  second  volume  appearing 
posthumously. 

238.  Pierre  Simon  Laplace,  the  son  of  a  small  farmer, 
was  born  at  Beaumont  in  Normandy  in  1749,  being  thus 
13  years  younger  than  his  great  rival  Lagrange.  Thanks 
to  the  help  of  well-to-do  neighbours,  he  was  first  a  pupil 
and  afterwards  a  teacher  at  the  Military  School  of  his 
native  town.  When  he  was  18  he  went  to  Paris  with  a 
letter  of  introduction  to  D'Alembert,  and,  when  no  notice 
was  taken  of  it,  wrote  him  a  letter  on  the  principles  of 
mechanics  which  impressed  D'Alembert  so  much  that  he 
at  once  took  interest  in  the  young  mathematician  and 
procured  him  an  appointment  at  the  Military  School  at 
Paris.  From  this  time  onwards  Laplace  lived  continuously 
at  Paris,  holding  various  official  positions.  His  first  paper 
(on  pure  mathematics)  was  published  in  the  Transactions 
of  the  Turin  Academy  for  the  years  1766-69,  and  from  this 
time  to  the  end  of  his  life  he  produced  an  uninterrupted 
series  of  papers  and  books  on  astronomy  and  allied  de- 
partments of  mathematics. 

Laplace's  work  on  astronomy  was  to  a  great  extent 
incorporated  in  his  Mecanique  Celeste,  the  five  volumes 
of  which  appeared  at  intervals  between  1799  an(^  ^25' 
In  this  great  treatise  he  aimed  at  summing  up  all  that  had 
been  done  in  developing  gravitational  astronomy  since  the 
time  of  Newton.  The  only  other  astronomical  book  which 
he  published  was  the  Exposition  du  Systeme  du  Monde 
(1796),  one  of  the  most  perfect  and  charmingly  written 
popular  treatises  on  astronomy  ever  published,  in  which 
the  great  mathematician  never  uses  either  an  algebraical 
formula  or  a  geometrical  diagram.  He  published  also  in 
1812  an  elaborate  treatise  on  the  theory  of  probability  or 
chance,t  on  which  nearly  all  later  developments  of  the 
subject  have  been  based,  and  in  1819  a  more  popular 
Essai  Philosophique  on  the  same  subject. 

,  *  Theorie  des  Fonctions  Analytiques  (i797)>  Resolution  des 
Equations  Nume'riques  (1798);  Lemons  sur  le  Calcul  des  Fonctions 
(1805).  *j~  Theorie  Analytique  des  Probabilites, 


[To  face  p.  307. 


$  238]  Life  of  Laplace  307 

Laplace's  personality  seems  to  have  been  less  attractive 
than  that  of  Lagrange.  He  was  vain  of  his  reputation  as 
a  mathematician  and  not  always  generous  to  rival  dis- 
coverers. To  Lagrange,  however,  he  was  always  friendly, 
and  he  was  also  kind  in  helping  young  mathematicians  of 
promise.  While  he  was  perfectly  honest  and  courageous 
in  upholding  his  scientific  and  philosophical  opinions,  his 
politics  bore  an  undoubted  resemblance  to  those  of  the 
Vicar  of  Bray,  and  were  professed  by  him  with  great 
success.  He  was  appointed  a  member  of  the  Commission 
for  Weights  and  Measures,  and  afterwards  of  the  Bureau  des 
Longitudes,  and  was  made  professor  at  the  Ecole  Normale 
when  it  was  founded.  When  Napoleon  became  First 
Consul,  Laplace  asked  for  and  obtained  the  post  of  Home 
Secretary,  but — fortunately  for  science — was  considered 
quite  incompetent,  and  had  to  retire  after  six  weeks 
(1799)*;  as  a  compensation  he  was  made  a  member  of 
the  newly  created  Senate.  The  third  volume  of  the 
Mecanique  Celeste,  published  in  1802,  contained  a  dedication 
to  the  "  Heroic  Pacificator  of  Europe,"  at  whose  hand  he 
subsequently  received  various  other  distinctions,  and  by  whom 
he  was  created  a  Count  when  the  Empire  was  formed.  On 
the  restoration  of  the  Bourbons  in  1814  he  tendered  his 
services  to  them,  and  was  subsequently  made  a  Marquis. 
In  1816  he  also  received  a  very  unusual  honour  for  a 
mathematician  (shared,  however,  by  D'Alembert)  by  being 
elected  one  of  the  Forty  "  Immortals "  of  the  Academic 
Fran$aise ;  this  distinction  he  seems  to  have  owed  in  great 
part  to  the  literary  excellence  of  the  Systime  du  Monde. 

Notwithstanding  these  distractions  he  worked  steadily 
at  mathematics  and  astronomy,  and  even  after  the  com- 
pletion of  the  Mecanique  Celeste  wrote  a  supplement  to  it 
which  was  published  after  his  death  (1827). 

His  last  words,  "  Ce  que  nous  connaissons  est peu  de  chose> 
(e  <jUJ  nous  ignorons  est  immense"  coming  as  they  did  from 
one  who  had  added  so  much  to  knowledge,  shew  his 
character  in  a  pleasanter  aspect  than  it  sometimes  pre- 
sented during  his  career. 

*  The  fact  that  the  post  was  then  given  by  Napoleon  to  his  brother 
Lucien  suggests  some  doubts  as  to  the  unprejudiced  character  of 
the  verdict  of  incompetence  pronounced  by  Napoleon  against  Laplace. 


308  A  Short  History  of  Astronomy  [CH.  xi. 

239.  With  the  exception  of  Lagrange's  paper  on  libration, 
nearly   all   his   and    Laplace's   important   contributions   to 
astronomy  were  made  when  Clairaut's   and   D'Alembert's 
work   was    nearly   finished,    though    Euler's   activity   con- 
tinued  for    nearly    20    years   more.     Lagrange,    however, 
survived  him  by  30  years  and  Laplace  by  more  than  40;  and 
together  they  carried  astronomical  science  to  a  far  higher 
stage  of  development  than  their  three  predecessors. 

240.  To   the   lunar   theory    Lagrange   contributed    com- 
paratively little  except  general  methods,  applicable  to  this 
as  to  other  problems  of  astronomy;  but  Laplace  devoted 
great  attention  to   it.    V)f  his   special  -discaveries_in   the 
subject  the  most  notable  was  his  explanation  of  the  seculaK 
acceleration  of  the  moon's  mean  motion  (chapter  x.,  §  201),) 
which    had  puzzled  so  many  astronomers.     Lagrange  had] 
attempted  to  explain  it   (1774),  and    had   failed   so   com- 
pletely that  he  was  inclined  to  discredit  the  early  observa- 
tions  on   which   the    existence    of   the   phenomenon   was 
based.       Laplace,    after    trying    ordinary   methods  without 
success,  attempted  to  explain  it  by  supposing  that  gravita- 
tion  was   an   effect    not    transmitted    instantaneously,    but 
that,  like  light,  it  took  time  to  travel  from  the  attracting 
body  to  the  attracted  one  ;   but  this  also  failed,  f.  Finally 
he  traced  it  (1787)  to  an  indirect  planetary^effectj)  For,  as  it 
happens,  certain  perturbations  which  the  moon  experiences 
owing    to    the    action    of   the   sun    depend    among   other 
things  on  the  eccentricity  of  the  earth's  orbit,;  this  is  one 
of  the   elements   (§  236)  which   is  being  altered   by   the 
action  of  the  planets,  and  has  for  many  centuries  been  very 
slowly  decreasing;  the  perturbation  in  question  is  there- 
fore being  very  slightly  altered,  and  the   moon's  average 
rate  of  motion  is  in  consequence  very  slowly  increasing,  or  V 
the  length  of  the  month  decreasing.     The  whole  effect  is   *\ 
excessively  minute,  and  only  becomes  perceptible  in  the 
course  of  a  long  time.     Laplace's  calculation  shewed  that 
the  moon  would,  in  the  course  of  a  century,  or  in  about 
1,300  complete  revolutions,  gain  about  10"  (more  exactly 
io"'2)  owing   to   this  cause,   so  that  her  place  in  the  sky 
would  differ  by  that  amount  from  what  it  would  be  if  this 
disturbing  cause  did  not  exist;  in  two  centuries  the  angle 
gained  would  be  40",  in  three  centuries  90",  and  so  on. 


§§  239-241]  Lunar  Theory  309 

This  may  be  otherwise  expressed  by  saying  that  the  length  \ 
of  the  month  diminishes  by  about  one-thirtieth  of  a  second  > 
in  the  course  of  a  century.     Moreover,  as  Laplace  shewed  ) 
(§  245),  the  eccentricity  of  the  earth's  orbit  will  not  go  orr 
diminishing  indefinitely,  but  after  an  immense  period  to  be 
reckoned  in  thousands  of  years  will  begin  to  increase,  and 
the  moon's  motion  will  again  become  slower  in  consequence. 

Laplace's  result  agreed  almost  exactly  with  that  indicated 
by  observation;  and  thus  the  last  known  discrepancy  01 
importance  in  the  solar  system  between  theory  and  observa- 
tion appeared  to  be  explained  away  ;  and  by  a  curious 
coincidence  this  was  effected  just  a  hundred  years  after  the 
publication  of  the  Principia. 

Many  years  afterwards,  however,  Laplace's  explanation 
was  shewn  to  be  far  less  complete  than  it  appeared  at  the 
time  (chapter  xin.,  §  287). 

The  same  investigation  revealed  to  Laplace  the  existence 
of  alterations  of  a  similar  character,  and  due  to  the  same 
cause,  of  other  elements  in  the  moon's  orbit,  which,  though 
not  previously  noticed,  were  found  to  be  indicated  by 
ancient  eclipse  observations. 

241.  The  third  volume  of  the  Mecanique  Celeste  con- 
tains a  general  treatment  of  the  lunar  theory,  based  on  a 
method  entirely  different  from  any  that  had  been  employed 
before,  and  worked  out  in  great  detail.  "  My  object,"  says 
Laplace,  "  in  this  book  is  to  exhibit  in  the  one  law  of 
universal  gravitation  the  source  of  all  the  inequalities  of 
the  motion  of  the  moon,  and  then  to  employ  this  law  as 
a  means  of  discovery,  to  perfect  the  theory  of  this  motion 
and  to  deduce  from  it  several  important  elements  in  the 
system  of  the  moon."  Laplace  himself  calculated  no  lunar 
tables,  but  the  Viennese  astronomer  John  Tobias  Burg 
(1766-1834)  made  considerable  use  of  his  formulae, 
together  with  an  immense  number  of  Greenwich  observa- 
tions, for  the  construction  of  lunar  tables,  which  were  sent 
to  the  Institute  of  France  in  1801  (before  the  publication 
of  Laplace's  complete  lunar  theory),  and  published  in  a 
slightly  amended  form  in  1806.  A  few  years  later  (1812) 
John  Charles  Burckhardt  (1773-1825),  a  German  who  had 
settled  in  Paris  and  worked  under  Laplace  and  Lalande, 
produced  a  new  set  of  tables  based  directly  on  the  formulae 


3io  A  Short  History  of  Astronomy  [CH.  XL 

of  the  Mecanique  Celeste.  These  were  generally  accepted 
in  lieu  of  Burg's,  which  had  been  in  their  turn  an  im- 
provement on  Mason's  and  Mayer's. 

Later  work  on  lunar  theory  may  conveniently  be  regarded 
as  belonging  to  a  new  period  of  astronomy  (chapter  xin., 
§  286). 

242.  Observation  had  shewn  the  existence  of  inequali- 
ties in  the  planetary  and  lunar  motions  which  seemed  to 
belong  to  two  different  classes.  On  the  one  hand  were 
inequalities,  such  as  most  of  those  of  the  moon,  which  went 
through  their  cycle  of  changes  in  a  single  revolution  or  a 
few  revolutions  of  the  disturbing  body ;  and  on  the  other 
such  inequalities  as  the  secular  acceleration  of  the  moon's 
mean  motion  or  the  motion  of  the  earth's  apses,  in  which 
a  continuous  disturbance  was  observed  always  acting  in  the 
same  direction,  and  shewing  no  signs  of  going  through  a 
periodic  cycle  of  changes. 

The  mathematical  treatmert  of  perturbations  soon  shewed 
the  desirability  of  adopting  different  methods  of  treatment 
for  two  classes  of  inequalities,  which  corresponded  roughly, 
though  not  exactly,  to  those  just  mentioned,  and  to  which 
the  names  of  periodic  and  secular  gradually  came  to  be 
attached.  The  distinction  plays  a  considerable  part  in 
Euler's  work  (§  236),  but  it  was  Lagrange  who  first 
recognised  its  full  importance,  particularly  for  planetary 
theory,  and  who  made  a  special  study  of  secular  inequalities. 

When  the  perturbations  of  one  planet  by  another  are 
being  studied,  it  becomes  necessary  to  obtain  a  mathematical 
expression  for  the  disturbing  force  which  the  second  planet 
exerts.  This  expression  depends  in  general  both  on  the 
elements  of  the  two  orbits,  and  on  the  positions  of  the 
planets  at  the  time  considered.  It  can,  however,  be  divided 
up  into  two  parts,  one  of  which  depends  on  the  positions  of  the 
planets  (as  well  as  on  the  elements),  while  the  other  depends 
only  on  the  elements  of  the  two  orbits,  and  is  independent  of 
the  positions  in  their  paths  which  the  planets  may  happen 
to  be  occupying  at  the  time.  Since  the  positions  of  planets 
in  their  orbits  change  rapidly,  the  former  part  of  the 
disturbing  force  changes  rapidly,  and  produces  in  general, 
at  short  intervals  of  time,  effects  in  opposite  directions,  first, 
for  example,  accelerating  and  then  retarding  the  motion  of 


$  242 J  Periodic  and  Secular  Inequalities  31! 

the  disturbed  planet ;  and  the  corresponding  inequalities  of"=S 
motion  are  the  periodic  inequalities,  which  for  the  most  part  // 
go  through  a  complete  cycle  of  changes  in  the  course  of  a  \ 
few  revolutions  of  the  planets,  or  even  more  rapidly.     The   \ 
other  part  of  the  disturbing  force  remains  nearly  unchanged    \, 
for  a  considerable  period,  and  gives  rise  to  changes  in  the     \ 
elements  which,  though  in  general  very  small,  remain  for  a     f 
long  time  without  sensible  alteration,  and  therefore  continu-    / 
ally  accumulate,  becoming  considerable  with  the  lapse  of  i' 
time  :  these  are  the  secular  inequalities. 

Speaking    generally,    we    may   say    that    the    periodical 
inequalities    are    temporary   and    the    secular    inequalities   I 
permanent    in    their    effects,    or    as    Sir  John    Herschely 
expresses  it : — 

"  The  secular  inequalities  are,  in  fact,  nothing  but  what  remains 
after  the  mutual  destruction  of  a  much  larger  amount  (as  it  very 
often  is)  of  periodical.  But  these  are  in  their  nature  transient  and 
temporary ;  they  disappear  in  short  periods,  and  leave  no  trace. 
The  planet  is  temporarily  withdrawn  from  its  orbit  (its  slowly 
varying  orbit),  but  forthwith  returns  to  it,  to  deviate  presently  as 
much  the  other  way,  while  the  varied  orbit  accommodates  and 
adjusts  itself  to  the  average  of  these  excursions  on  either  side 
of  it."  * 

"  Temporary  "  and  "  short "  are,  however,  relative  terms. 
Some  periodical  inequalities,  notably  in  the  case  of  the 
moon,  have  periods  of  only  a  few  days,  and  the  majority 
which  are  of  importance  extend  only  over  a  few  years  ;  but 
some  are  known  which  last  for  centuries  or  even  thousands 
of  years,  and  can  often  be  treated  as  secular  when  we  only 
want  to  consider  an  interval  of  a  few  years.  On  the  other 
hand,  most  of  the  known  secular  inequalities  are  not  really 
]  er  nanent,  but  fluctuate  like  the  periodical  ones,  though 
only  in  the  course  of  immense  periods  of  time  to  be  reckoned 
usually  by  tens  of  thousands  of  years. 

One  distinction  between  the  lunar-  and  planetary  theories 
is  that  in  the  former  periodic  inequalities  are  comparatively 
large  and,  especially  for  practical  purposes  such  as  computing 
the  position  of  the  moon  a  few  months  hence,  of  great 

*  Outlines  of  Astronomy,  §  656. 


312  A  Short  History  of  Astronomy  [Cn.  XT. 

importance  ;  whereas  the  periodic  inequalities  of  the  planets 
are  generally  small  and  the  secular  inequalities  are  the  most 
interesting. 

The  method  of  treating  the  elements  of  the  elliptic  orbits 
as  variable  is  specially  suitable  for  secular  inequalities  ;  but 
for  periodic  inequalities  it  is  generally  better  to  treat  the 
body  as  being  disturbed  from  an  elliptic  path,  and  to  study 
these  deviations. 

"  The  simplest  way  of  regarding  these  various  perturbations 
consists  in  imagining  a  planet  moving  in  accordance  with  the  laws 
of  elliptic  motion,  on  an  ellipse  the  elements  of  which  vary  by 
insensible  degrees ;  and  to  conceive  at  the  same  time  that  the 
true  planet  oscillates  round  this  fictitious  planet  in  a  very  small 
orbit  the  nature  of  which  depends  on  its  periodic  perturbations."  * 

The  former  method,  due  as  we  have  seen  in  great  measure 
to  Euler,  was  perfected  and  very  generally  used  by  Lagrange, 
and  often  bears  his  name. 

^3.  It  was  at  first  naturally  supposed  that  the  slow 
alteration  in  the  rates  of  the  motions  of  Jupiter  and  Saturn 
(§§  235>  236,  and  chapter  x.,  §  204)  was  a  secular  inequality ; 
Lagrange  in  1766  made  an  attempt  to  explain  it  on  this 
basis  which,  though  still  unsuccessful,  represented  the 
observations  better  than  Euler's  work.  Laplace  in  his  first 
paper  on  secular  inequalities  (1773)  found  by  the  use  tf 
a  more  complete  analysis  that  the  secular  alterations  in 
the  rates  of  motions  of  Jupiter  and  Saturn  appeared  to 
vanish  entirely,  and  attempted  to  explain  the  motions  by  the 
hypothesis,  so  often  used  by  astronomers  when  in  difficulties, 
that  a  comet  had  been  the  cause. 

I*1  J773  John  Henry  Lambert  (1728-1777)  discovered 
from  a  study  of  observations  that,  whereas  HalJey  had  found 
Saturn  to  be  moving  more  slowly  than  in  ancient  times,  it 
was  now  moving  faster  than  in  Halley's  time — a  conclusion 
which  pointed  to  a  fluctuating  or  periodic  cause  of  some 
kind. 

Finally  in  1784  Laplace  arrived  at  the  true  explanation.      \ 
Lagrange  had  observed  in   1776  that  if  the  times  of  revo- 
lution of  two  planets  are  exactly  proportional  to  two  whole 

*  Laplace,  Systeme  du  Monde. 


tt  243,  244]  Long  Inequalities  313 

numbers,  then  part  of  the  periodic  disturbing  force  produces 
a  secular  change  in  their  motions,  acting  continually  in  the  \ 
same  direction ;  though  he  pointed  out  that  such  a  case  J 
did  not  occur  in  the  solar  system.  If  moreover  the  times 
of  revolution  are  nearly  proportional  to  two  whole  numbers 
(neither  of  which  is  very  large),  then  part  of  the  periodic 
disturbing  force  produces  an  irregularity  that  is  not  strictly 
secular,  but  has  a  very  long  period  ;  and  a  disturbing  force 
so  small  as  to  be  capable  of  being  ordinarily  overlooked 
may,  if  it  is  of  this  kind,  be  capable  of  producing  a  con- 
siderable effect.*  Now  Jupiter  and  Saturn  revolve  round 
the  sun  in  about  4,  todays  and  10,759  days  respectively;  five 
times  the  former  number  is  2i,665x_and  twjce^the  latter  is 
21,518,  which  isjvery  little less^.  Consequently  tneexcepihsnal 
case  occurs ;  anH  on  womng  it  out  Laplace  found  an 
appreciable  inequality  with  a  period  of  about  900  years,  ^ 
which  explained  the  observations  satisfactorily. 

The  inequalities  of  this  class,  of  which  several  others  have  \ 
been  discovered,  are  known  as  long  inequalities,  and  may     T 
be  regarded  as  connecting  links  between  secular  inequalities/ 

and  periodical  inequalities  of  the  usual  kind.          - — 

434^  ^ 'he^~discovery~  that  tKe^observed  inequality  of 
Jupiter  and  Saturn  was  not  secular  may  be  regarded  as 
the  first  step  in  a  remarkable  series  of  investigations  on 
secular  inequalities  carried  out  by  Lagrange  and  Laplace, 
for  the  most  part  between  1773  and  1784,  leading  to  some 
of  the  most  interesting  and  general  results  in  the  whole  of 
gravitational  astronomy.  The  two  astronomers,  though 
living  respectively  in  Berlin  and  Paris,  were  in  constant 

*  If  n,  n'  are  the  mean  motions  of  the  two  planets,  the  expression 
for  the  disturbing  force  contains  terms  of  the  type  =  (n  p±  n'  p')  t, 

where  p,  p'  are  integers,  and  the  coefficient  is  of  the  order  p  r~^  p' 
in  the  eccentricities  and  inclinations.  If  now  p  and  />'  are  such 
that  np  r^,  n'  p'  is  small,  the  corresponding  inequality  has  a  perio  I 
2  TT/  (np  r^,  n'  p'),  and  though  its  coefficient  is  of  order/)  ^-/>',  it 
has  the  small  factor  np  r^s  n  p'  (or  its  square)  in  the  denominator  and 
may  therefore  be  considerable.  In  the  case  of  Jupiter  and  Saturn, 
for  example,  n  =  109.257  in  seconds  of  arc  per  annum,  n'  =  43,996; 
5  n'  —  2n  =  1,466;  there  is  therefore  an  inequality  of  the  third  order, 

with  a  period  (in  years)  = Tl  =  900. 

Ij&OQ 


314  -A  Short  History  of  Astronomy  [CH.  xi, 

communication,  and  scarcely  any  important  advance  was 
made  by  the  one  which  was  not  at  once  utilised  and 
developed  by  the  other. 

The  central  problem  was  that  of  the  secular  alterations 
in  the  elements  of  a  planet's  orbit  regarded  as  a  varying 
ellipse.  Three  of  these  elements,  the  axis  of  the  ellipse, 
its  eccentricity,  and  the  inclination  of  its  plane  to  a  fixed 
plane  (usually  the  ecliptic),  are  of  much  greater  importance 
than  the  other  three.  The  first  two  are  the  elements  on 
which  the  size  and  shape  of  the  orbit  depend,  and  the  first 
also  determines  (by  Kepler's  Third  Law)  the  period  of 
revolution  and  average  rate  of  motion  of  the  planet ;  *  the 
third  has  an  important  influence  on  the  mutual  relations  of 
the  two  planets.  The  other  three  elements  are  chiefly  of 
importance  for  periodical  inequalities. 

It  should  be  noted  moreover  that  the  eccentricities  and 
inclinations  were  in  all  cases  (except  those  specially  men- 
tioned) considered  as  small  quantities ;  and  thus  all  t  e 
investigations  were  approximate,  these  quantities  and  the 
disturbing  forces  themselves  being  treated  as  small. 
^Sjj^The  basis  of  the  whole  series  of  investigations  was  a 
longTpaper  published  by  Lagrange  in  1766,  in  which  he 
explained  the  method  of  variation  of  elements,  and  gave 
formulae  connecting  their  rates  of  change  with  the  disturbing 
forces. 

In  his  paper  of  1773  Laplace  found  that  what  was  true  of 
Jupiter  and  Saturn  had  a  more  general  application,  and 
proved  that  in  the  case  of  any  planet,  disturbed  by  any 
other,  the  axis  was  not  only  undergoing  no  secular  change 
at  the  present  time,  but  could  not  have  altered  appreciably 
since  "  the  time  when  astronomy  began  to  be  cultivated." 

In  the  next  year  Lagrange  obtained  an  expression  for  the 
secular  change  in  the  inclination,  valid  for  all  time.  When 
this  was  applied  to  the  case  of  Jupiter  and  Saturn,  which  on 
account  of  their  superiority  in  size  and  great  distance  from 
the  other  planets  could  be  reasonably  treated  as  forming 
with  the  sun  a  separate  system,  it  appeared  that  the  changes 
in  the  inclinations  would  always  be  of  a  periodic  nature,  so 

*  This  statement  requires  some  qualification  when  perturbations 
are  taken  into  account.  But  the  point  is  not  very  important,  and 
is  too  technical  to  be  discussed. 


*  245]  Stability  of  the  Solar  System  3 1 5 

that  they  could  never  pass  beyond  certain  fixed  limits,  not 
differing  much  from  the  existing  values.  The  like  result 
held  for  the  system  formed  by  the  sun,  Venus,  the  earth, 
and  Mars.  Lagrange  noticed  moreover  that  there  were 
cases,  which,  as  he  said,  fortunately  did  not  appear  to  exist 
in  the  system  of  the  world,  in  which,  on  the  contrary,  the 
inclinations  might  increase  indefinitely.  The  distinction 
depended  on  the  masses  of  the  bodies  in  question ;  and 
although  all  the  planetary  masses  were  somewhat  uncertain, 
and  those  assumed  by  Lagrange  for  Venus  and  Mars  almost 
wholly  conjectural,  it  did  not  appear  that  any  reasonable 
alteration  in  the  estimated  masses  would  affect  the  general 
conclusion  arrived  at. 

Two  years  later  (1775)  Laplace,  much  struck  by  the 
method  which  Lagrange  had  used,  applied  it  to  the  dis- 
cussion of  the  secular  variations  of  the  eccentricity,  and 
found  that  these  were  also  of  a  periodic  nature,  so  that  the 
eccentricity  also  could  not  increase  or  decrease  indefinitely. 

In  the  next  year  Lagrange,  in  a  remarkable  paper  of 
only  14  pages,  proved  that  whether  the  eccentricities  and 
inclinations  were  treated  as  small  or  not,  and  whatever  the 
masses  of  the  planets  might  be,  the  changes  in  the  length  of 
the  axis  of  any  planetary  orbit  were  necessarily  all  periodic, 
so  that  for  all  time  the  length  of  the  axis  could  only  fluctu- 
ate between  certain  definite  limits.  This  result  was,  however, 
still  based  on  the  assumption  that  the  disturbing  forces 
could  be  treated  as  small. 

Next  came  a  series  of  five  papers  published  between  1781 
and  1784  in  which  Lagrange  summed  up  his  earlier  work, 
revised  and  improved  his  methods,  and  applied  them  to 
periodical  inequalities  and  to  various  other  problems. 

Lastly  in  1784  Laplace,  in  .the  same  paper  in  which  he 
explained  the  long  inequality  of  Jupiter  and  Saturn,  es- 
tablished by  an  extremely  simple  method  two  remarkable 
relations  between  the  eccentricities  and  inclinations  of  the 
planets,  or  any  similar  set  of  bodies. 

The  first  relation  is  :— 

If  the  mass  of  each  planet  be  multiplied  by  the  square  root 
of  the  axis  of  its  orbit  and  by  the  square  of  the  eccentricity, 
then  the  sum  of  these  products  for  all  the  planets  is  invariable 
save  for  periodical  inequalities. 


316  A  Short  History  of  Astronomy  [CH.  XI. 

The  second  is  precisely  similar,  save  that  eccentricity  is 
replaced  by  inclination.* 

The  first  of  these  propositions  establishes  the  existence 
of  what  may  be  called  a  stock  or  fund  of  eccentricity  shared 
by  the  planets  of  the  solar  system.  If  the  eccentricity  of 
any  one  orbit  increases,  that  of  some  other  orbit  must 
undergo  a  corresponding  decrease.  Also  the  fund  can 
never  be  overdrawn.  Moreover  observation  shews  that  the 
eccentricities  of  all  the  planetary  orbits  are  small ;  conse- 
quently the  whole  fund  is  small,  and  the  share  owned  at 
any  time  by  any  one  planet  must  be  small. t  Consequently 
the  eccentricity  of  the  orbit  of  a  planet  of  which  the  mass 
and  distance  from  the  sun  are  considerable  can  never 
increase  much,  and  a  similar  conclusion  holds  for  the 
inclinations  of  the  various  orbits. 

One  remarkable  characteristic  of  the  solar  system  is 
presupposed  in  these  two  propositions ;  namely,  that  all  the 
planets  revolve  round  the  sun  in  the  same  direction,  which 
to  an  observer  supposed  to  be  on  the  north  side  of  the 
orbits  appears  to  be  contrary  to  that  in  which  the  hands 
of  a  clock  move.  If  any  planet  moved  in  the  opposite 
direction,  the  corresponding  parts  of  the  eccentricity  and 
inclination  funds  would  have  to  be  subtracted  instead  of 
being  added ;  and  there  would  be  nothing  to  prevent  the 
fund  from  being  overdrawn. 

A  somewhat  similar  restriction  is  involved  in  Laplace's 
earlier  results  as  to  the  impossibility  of  permanent  changes 
in  the  eccentricities,  though  a  system  might  exist  in  which 
his  result  would  still  be  true  if  one  or  more  of  its  members 
revolved  in  a  different  direction  from  the  rest,  but  in  this 
case  there  would  have  to  be  certain  restrictions  on  the 
proportions  of  the  orbits  not  required  in  the  other  case. 

*  S  rm  */a  =  c,  S  tari*im  Va  =  S,  where  m  is  the  mass  of  any 
planet,  a,  e,  i  are  the  semi-major  axis,  eccentricity,  and  inclination 
of  the  orbit.  The  equation  is  true  as  far  as  squares  of  small 
quantities,  and  therefore  it  is  indifferent  whether  or  not  tan  i  is 
replaced  as  in  the  text  by  i. 

f  Nearly  the  whole  of  the  "  eccentricity  fund "  and  of  the 
"inclination  fund"  of  the  solar  system  is  shared  between  Jupiter 
and  Saturn.  If  Jupiter  were  to  absorb  the  whole  of  each  fund,  the 
eccentricity  of  its  orbit  would  only  be  increased  by  about  25  per 
cent.,  and  the  inclination  to  the  ecliptic  would  not  be  doubled. 


§  245]  Stability  of  the  Solar  System  317 

Stated  briefly,  the  results  established  by  the  two  astro- 
nomers were  that  the  changes  in  axis,  eccentricity,  and 
inclination  of  any  planetary  orbit  are  all  permanently  re- 
stricted within  certain  definite  limits.  The  perturbations 
caused  by  the  planets  make  all  these  quantities  undergo 
fluctuations  of  limited  extent,  some  of  which,  caused  by  the 
periodic  disturbing  forces,  go  through  their  changes  in 
comparatively  short  periods,  while  others,  due  to  secular 
forces,  require  vast  intervals  of  time  for  their  completion. 

It  may  thus  be  said  that  the  stability  of  the  solar  system 
was  established,  as  far  as  regards  the  particular  astronomical 
causes  taken  into  account. 

Moreover,  if  we  take  the  case  of  the  earth,  as  an  in- 
habited planet,  any  large  alteration  in  the  axis,  that  is  in 
the  average  distance  from  the  sun,  would  produce  a  more 
than  proportional  change  in  the  amount  of  heat  and  light 
received  from  the  sun  ;  any  great  increase  in  the  eccentricity 
would  increase  largely  that  part  (at  present  very  small)  of 
our  seasonal  variations  of  heat  and  cold  which  are  due  to 
varying  distance  from  the  sun  ;  while  any  change  in  position 
of  the  ecliptic,  which  was  unaccompanied  by  a  corresponding 
change  of  the  equator,  and  had  the  effect  of  increasing  the 
angle  between  the  two,  would  largely  increase  the  variations  of 
temperature  in  the  course  of  the  year.  The  stability  shewn 
to  exist  is  therefore  a  guarantee  against  certain  kinds  of 
great  climatic  alterations  which  might  seriously  affect  the 
habitability  of  the  earth. 

It  is  perhaps  just  worth  while  to  point  out  that  the 
results  established  by  Lagrange  and  Laplace  were  mathe- 
matical consequences,  obtained  by  processes  involving  the 
neglect  of  certain  small  quantities  and  therefore  not  perfectly 
rigorous,  of  certain  definite  hypotheses  to  which  the  actual 
conditions  of  the  solar  system  bear  a  tolerably  close  re- 
semblance. Apart  from  causes  at  present  unforeseen,  it  is 
therefore  not  unreasonable  to  expect  that  for  a  very  con- 
siderable period  of  time  the  motions  of  the  actual  bodies 
forming  the  solar  system  may  be  very  nearly  in  accordance 
with  these  results  ;  but  there  is  no  valid  reason  why  certain  dis- 
turbing causes,  ignored  or  rejected  by  Laplace  and  Lagrange 
on  account  of  their  insignificance,  should  not  sooner  or  later 
produce  quite  appreciable  effects  (cf.  chapter  xin.,  §  293). 


318  A   Short  History  of  Astronomy  [Cu.  xi. 

246.  A  few  of  Laplace's  numerical  results  as  to  the  secular 
variations   of  the  element*  may  serve  to  give  an  idea  of 
the  magnitudes  dealt  with. 

The  line  of  apses  of  each  planet  moves  in  the  same 
direction ;  the  most  rapid  motion,  occurring  in  the  case  of 
Saturn,  amounted  to  about  15"  per  annum,  or  rather  less 
than  half  a  degree  in  a  century.  If  this  motion  were  to 
continue  uniformly,  the  line  of  apses  would  require  no  less 
than  80,000  years  to  perform  a  complete  circuit  and  return 
to  its  original  position.  The  motion  of  the  line  of  nodes 
(or  line  in  which  the  plane  of  the  planet's  orbit  meets  that 
of  the  ecliptic)  was  in  general  found  to  be  rather  more 
rapid.  The  annual  alteration  in  the  inclination  of  any  orbit 
to  the  ecliptic  in  no  case  exceeded  a  fraction  of  a  second  ; 
while  the  change  of  eccentricity  of  Saturn's  orbit,  which 
was  considerably  the  largest,  would,  if  continued  for  four 
centuries,  have  only  amounted  to  T^V^- 

247.  The   theory  of  the   secular   inequalities   has   been 
treated  at  some  length  on  account  of  the  general  nature  of 
the  results  obtained.     For  the  purpose   of  predicting  the 
places  of  the  planets  at  moderate  distances  of  time  the 
periodical  inequalities  are,  however,  of  greater  importance. 
These  were  also  discussed  very  fully  both  by  Lagrange  and 
Laplace,  the  detailed  working  out  in  a  form  suitable  for 
numerical  calculation  being  largely  due  to  the  latter.     From 
the  formulae  given  by  Laplace  and  collected  in  the  Mecanique 
Celeste    several   sets   of    solar   and    planetary   tables   were 
calculated,  which  were  in  general  found  to  represent  closely 
the  observed  motions,  and  which   superseded  the   earlier 
tables  based  on  less  developed  theories.* 

248.  In   addition   to    the   lunar   and   planetary   theories 
nearly  all  the  minor  problems  of  gravitational  astronomy 
were  rediscussed  by  Laplace,  in  many  cases  with  the  aid 
of  methods  due  to  Lagrange,  and  their  solution  was  in  all 
cases  advanced. 

The  theory  of  Jupiter's  satellites,  which  with  Jupiter  form 

• 

*  Of  tables  based  on  Laplace's  work  and  published  up  to  the  time 
of  his  death,  the  chief  solar  ones  were  those  of  von  Zach  (1804)  and 
Delambre  (1806)  ;  and  the  chief  planetary  ones  were  those  of 
Lalande  (1771),  of  Lindenau  for  Venus,  Mars,  and  Mercury  (1810-13), 
and  of  Bouvardiov  Jupiter,  Saturn,  and  Uranus  (1808  and  1821). 


$$246—249]     Planetary  Theory:  Minor  Problems  319 

a  sort  of  miniature  solar  system  but  with  several  character- 
istic peculiarities,  was  fully  dealt  with ;  the  other  satellites 
received  a  less  complete  discussion.  Some  progress  was 
also  made  with  the  theory  of  Saturn's  ring  by  shewing  that 
it  could  not  be  a  uniform  solid  body. 

Precession  and  nutation  were  treated  much  more  com- 
pletely than  by  D'Alembert ;  and  the  allied  problems  of 
the  irregularities  in  the  rotation  of  the  moon  and  of  Saturn's 
ring  were  also  dealt  with. 

The  figure  of  the  earth  was  considered  in  a  much  more 
general  way  than  by  Clairaut,  without,  however,  upsetting 
the  substantial  accuracy  of  his  conclusions  ;  and  the  theory 
of  the  tides  was  entirely  reconstructed  and  greatly  improved, 
though  a  considerable  gap  between  theory  and  observation 
still  remained. 

The  theory  of  perturbations  was  also  modified  so  as  to 
be  applicable  to  comets,  and  from  observation  of  a  comet 
(known  as  Lexell's)  which  had  appeared  in  1770  and  was 
found  to  have  passed  close  to  Jupiter  in  1767  it  was  inferred 
that  its  orbit  had  been  completely  changed  by  the  attraction 
of  Jupiter,  but  that,  on  the  other  hand,  it  was  incapable  of 
exercising  any  appreciable  disturbing  influence  on  Jupiter 
or  its  satellites. 

As,  on  the  one  hand,  the  complete  calculation  of  the 
perturbations  of  the  various  bodies  of  the  solar  system 
presupposes  a  knowledge  of  their  masses,  so  reciprocally 
if  the  magnitudes  of  these  disturbances  can  be  obtained 
from  observation  they  can  be  used  to  determine  or  to 
correct  the  values  of  the  several  masses.  In  this  way  the 
masses  of  Mars  and  of  Jupiter's  satellites,  as  well  as  of 
Venus  (§  235),  were  estimated,  and  those  of  the  moon  and 
the  other  planets  revised.  In  the  case  of  Mercury,  however, 
no  perturbation  of  any  other  planet  by  it  could  be  satis- 
factorily observed,  and — except  that  it  was  known  to  be  small 
— its  mass  remained  for  a  long  time  a  matter  of  conjecture. 
It  was  only  some  years  after  Laplace's  death -that  the  effect 
produced  by  it  on  a  comet  enabied  its  mass  to  be  estimated 
(1842),  and  the  mass  is  even  now  very  uncertain. 

249.  By  the  work  of  the  great  mathematical  astronomers 
of  the  1 8th  century,  the-  results  of  which  were  summarised 
in  the  Mecanique  Celeste,  it  was  shewn  to  be  possible  to 


320  A  Short  History  of  Astronomy  [Cn.  XI. 

account  for  the  observed  motions  of  the  bodies  of  the  solar 
system  with  a  tolerable  degree  of  accuracy  by  means  of  the 
law  of  gravitation. 

Newton's  problem  (§  228)  was  therefore  approximately 
solved,  and  the  agreement  between  theory  and  observation 
was  in  most  cases  close  enough  for  the  practical  purpose 
of  predicting  for  a  moderate  time  the  places  of  the  various 
celestial  bodies.  The  outstanding  discrepancies  between 
theory  and  observation  were  for  the  most  part  so  small  as 
compared  with  those  that  had  already  been  removed  as  to 
leave  an  almost  universal  conviction  that  they  were  capable 
of  explanation  as  due  to  errors  of  observation,  to  want 
of  exactness  in  calculation,  or  to  some  similar  cause. 

250.  Outside  the  circle  of  professed  astronomers  and 
mathematicians  Laplace  is  best  known,  not  as  the  author  of 
the  Mecanique  Celeste,  but  as  the  inventor  of  the 


____  ^ 

This  famous  speculation  was  published  (in  1796)  in  hij^ 
popular  book   the  Systbne   du  Monde  already   mentioned,  \ 
and  was  almost  certainly  independent  of  a  somewhat  similar    > 
but  less  detailed  theory  which  had  been  suggested  by  the  ) 
philosopher  Immanuel  Kant  in  1755. 

Laplace  was  struck  with  certain  remarkable  characteristics 
of  the  solar  system.  The  seven  planets  known  to  him  when 
he  wrote  revolved  round  the  sun  in  the  same  direction,  the 
fourteen  satellites  revolved  round  their  primaries  still  in 
the  same  direction,*  and  such  motions  of  rotation  of  sun, 
planets,  and  satellites  about  their  axes  as  were  known 
followed  the  same  law.  There  were  thus  some  30  or  40 
motions  all  in  the  same  direction.  If  these  motions  of  the 
several  bodies  were  regarded  as  the  result  of  chance  and 
were  independent  of  one  another,  this  uniformity  would  be 
a  coincidence  of  a  most  extraordinary  character,  as  unlikely 
as  that  a  coin  when  tossed  the  like  number  of  times  should 
invariably  come  down  with  the  same  face  uppermost. 

These  motions  of  rotation  and  revolution  were  moreover 
all  in  planes  but  slightly  inclined  to  one  another  ;  and  the 

*  The  motion  of  the  satellites  of  Uranus  (chapter  xn.,  §§  253,  255) 
is  in  the  opposite  direction.  When  Laplace  first  published  his  theory 
their  motion  was  doubtful,  and  he  does  not  appear  to  have  thought 
it  worth  while  to  notice  the  exception  in  later  editions  of  his  book, 


$  25o]  The  Nebular  Hypothesis  321 

eccentricities  of  all  the  orbits  were  quite  small,  so  that 
they  were  nearly  circular. 

Comets,  on  the  other  hand,  presented  none  of  these  pecu- 
liarities ;  their  paths  were  very  eccentric,  they  were  inclined 
at  all  angles  to  the  ecliptic,  and  were  described  in  either 
direction. 

Moreover  there  were  no  known  bodies  forming  a  con- 
necting link  in  these  respects  between  comets  and  planets 
or  satellites.* 

From  these  remarkable  coincidences  Laplace  inferred 
that  the  various  bodies  of  the  solar  system  must  have  had 
some  common  origin.  The  hypothesis  which  he  suggested 
was  that  they  had  condensed  out  of  a  body  that  might 
be  regarded  either  as  the  sun  with  a  vast  atmosphere  filling 
the  space  now  occupied  by  the  solar  system,  or  as  a  fluid 
mass  with  a  more  or  less  condensed  central  part  or  nucleus ; 
while  at  an  earlier  stage  the  central  condensation  might  have 
been  almost  non-existent. 

Observations  of  Herschel's  (chapter  xu.,  §§  259-61)  had 
recently  revealed  the  existence  of  many  hundreds  of  bodies 
known  as  nebulae,  presenting  very  nearly  such  appearances 
as  might  have  been  expected  from  Laplace's  primitive  body. 
The  differences  in  structure  which  they  shewed,  some  being 
apparently  almost  structureless  masses  of  some  extremely 
diffused  substance,  while  others  shewed  decided  signs  of 
central  condensation,  and  others  again  looked  like  ordinary 
stars  with  a  slight  atmosphere  round  them,  were  also 
strongly  suggestive  of  successive  stages  in  some  process 
of  condensation. 

Laplace's  suggestion  then  was  that  the  solar  system  had 
been  formed  by  condensation  out  of  a  nebula ;  and  a 
similar  explanation  would  apply  to  the  fixed  stars,  with  the 
planets  (if  any)  which  surrounded  them. 

He  then  sketched,  in  a  somewhat  imaginative  way,  the 
process  whereby  a  nebula,  if  once  endowed  with  a  rotatory 
motion,  might,  as  it  condensed,  throw  off  a  series  of  rings, 

*  This  statement  again  has  to  be  modified  in  consequence  of  the 
discoveries,  beginning  on  January  1st,  1801,  of  the  minor  planets 
(chapter  xin.,  §  294),  many  of  which  have  orbits  that  are  far  more 
eccentric  than  those  of  the  other  planets  and  are  inclined  to  the 
ecliptic  at  considerable  angles. 

21 


322  A  Short  History  of  Astronomy     I.CH.  XL,  §  250 

and  each  of  these  might  in  turn  condense  into  a  planet  with 
or  without  satellites  ;  and  gave  on  this  hypothesis  plausible 
reasons  for  many  of  the  peculiarities  of  the  solar  system. 

So  little  is,  however,  known  of  the  behaviour  of  a  body 
like  Laplace's  nebula  when  condensing  and  rotating  that  it 
is  hardly  worth  while  to  consider  the  details  of  the  scheme. 

That  Laplace  himself,  who  has  never  been  accused  of 
underrating  the  importance  of  his  own  discoveries,  did  not 
take  the  details  of  his  hypothesis  nearly  as  seriously  as 
many  of  its  expounders,  may  be  inferred  both  from  the  fact 
that  he  only  published  it  in  a  popular  book,  and  from  his 
remarkable  description  of  it  as  "these  conjectures  on  the 
formation  of  the  stars  and  of  the  solar  system,  conjectures 
which  I  present  with  all  the  distrust  (defiance)  which  every- 
thing which  is  not  a  result  of  observation  or  of  calculation 
ought  to  inspire."  * 

*  Systeme  du  Monde,  Book  V.,  chapter  vi. 


CHAPTER  XII. 

HERSCHEL. 

"Coelorum  perrupit  claustra." 

HERSCHEL'S  Epitaph. 

251.  Frederick  William  Herschel  was  born  at  Hanover  on 
November  i5th,  1738,  two  years  after  Lagrange  and  nine 
years  before  Laplace.  His  father  was  a  musician  in  the 
Hanoverian  army,  and  the  son,  who  shewed  a  remarkable 
aptitude  for  music  as  well  as  a  decided  taste  for  knowledge 
of  various  sorts,  entered  his  father's  profession  as  a  boy  (1753) 
On  the  breaking  out  of  the  Seven  Years'  War  he  served 
during  part  of  a  campaign,  but  his  health  being  delicate  his 
parents  "  determined  to  remove  him  from  the  service — a 
step  attended  by  no  small  difficulties,"  and  he  was  ac- 
cordingly sent  to  England  (1757),  to  seek  his  fortune  as  a 
musician. 

After  some  years  spent  in  various  parts  of  the  country,  he 
moved  (1766)  to  Bath,  then  one  of  the  great  centres  of 
fashion  in  England.  At  first  oboist  in  Linley's  orchestra, 
then  organist  of  the  Octagon  Chapel,  he  rapidly  rose  to 
a  position  of  great  popularity  and  distinction,  both  as  a 
musician  and  as  a  music-teacher.  He  played,  conducted, 
and  composed,  and  his  private  pupils  increased  so  rapidly 
that  the  number  of  lessons  which  he  gave  was  at  one  time 
35  a  week.  But  this  activity  by  no  means  exhausted 
his  extraordinary  energy;  he  had  never  lost  his  taste  for 
study,  and,  according  to  a  contemporary  biographer,  "  after 
a  fatiguing  day  of  14  or  16  hours  spent  in  his  vocation,  he 
would  retire  at  night  with  the  greatest  avidity  to  unbend  the 
mind,  if  it  may  be  so  called,  with  a  few  propositions  in 
Maclaurin's  Fluxions,  or  other  books  of  that  sort."  His 

323 


324  A  Short  History  of  Astronomy  [CH.  xil. 

musical  studies  had  long  ago  given  him  an  interest  in 
mathematics,  and  it  seems  likely  that  the  study  of  Robert 
Smith's  Harmonics  led  him  to  the  Compleat  System  of  Optics 
of  the  same  author,  and  so  to  an  interest  in  the  construction 
and  use  of  telescopes.  The  astronomy  that  he  read  soon 
gave  him  a  desire  to  see  for  himself  what  the  books  de- 
scribed;  first  he  hired  a  small  reflecting  telescope,  then 
thought  of  buying  a  larger  instrument,  but  found  that  the 
price  was  prohibitive.  Thus  he  was  gradually  led  to  attempt 
the  construction  of  his  own  telescopes  (1773).  His  brother 
Alexander,  for  whom  he  had  found  musical  work  at  Bath, 
arid  who  seems  to  have  had  considerable  mechanical  talent 
but  none  of  William's  perseverance,  helped  him  in  this 
undertaking,  while  his  devoted  sister  Caroline  (1750-1848), 
who  had  been  brought  over  to  England  by  William  in 
1772,  not  only  kept  house,  but  rendered  a  multitude  of 

^minor   services.     The  operation  of  grinding  and  polishing 

V  the  mirror  for  a  telescope  was  one  of  the  greatest  delicacy, 
and  at  a  certain  stage  required  continuous  labour  for 
several  hours.  On  one  occasion  Herschel's  hand  never  left 
the  polishing  tool  for  16  hours,  so  that  "by  way  of  keeping 
him  alive  "  Caroline  was  "  obliged  to  feed  him  by  putting 
the  victuals  by  bits  into  his  mouth,"  and  in  less  extreme 
cases  she  helped  to  make  the  operation  less  tedious  by 

i  reading  aloud  :  it  is  with  some  feeling  of  relief  that  we  hear 
that  on  these  occasions  the  books  read  were  not  on  mathe- 
matics, optics,  or  astronomy,  but  were  such  as  Don 

\  Quixote,  the  Arabian  Nights,  and  the  novels  of  Sterne  and 

LFielding. 

252.  After  an  immense  number  of  failures  Herschel 
succeeded  in  constructing  a  tolerable  reflecting  telescope- 
soon  to  be  followed  by  others  of  greater  size  and  perfection 
— and  with  this  he  made  his  first  recorded  observation,  of 
the  Orion  nebula,  in  March  1774. 

This  observation,  made  when  he  was  in  his  36th  year, 
may  be  conveniently  regarded  as  the  beginning  of  his 
astronomical  career,  though  for  several  years  more  music 
remained  his  profession,  and  astronomy  could  only  be 
cultivated  in  such  leisure  time  as  he  could  find  or  make 
for  himself;  his  biographers  give  vivid  pictures  of  his 
extraordinary  activity  during  this  period,  and  of  his  zeal 


to  252,  253]  HerscheVs  Early  Life  325 

in  using  odd  fragments  of  time,  such  as  intervals  between 
the  acts  at  a  theatre,  for  his  beloved  telescopes. 

A  letter  written  by  him  in  1783  gives  a  good  account  of 
the  spirit  in  which  he  was  at  this  time  carrying  out  his 
astronomical  work : — 

"  I  determined  to  accept  nothing  on  faith,  but  to  see  with  my 
own  eyes  what  others  had  seen  before  me.  ...  I  finally  suc- 
ceeded in  completing  a  so-called  Newtonian  instrument,  7  feet 
in  length.  From  this  I  advanced  to  one  of  10  feet,  and  at  last 
to  one  of  20,  for  I  had  fully  made  up  my  mind  to  carry  on 
the  improvement  of  my  telescopes  as  far  as  it  could  possibly  be 
done.  When  I  had  carefully  and  thoroughly  perfected  the  great 
instrument  in  all  its  parts,  I  made  systematic  use  of  it  in  my 
observations  of  the  heavens,  first  forming  a  determination  never 
to  pass  by  any,  the  smallest,  portion  of  them  without  due 
investigation." 

In  accordance  with  this  last  resolution  he  executed  on 
four  separate  occasions,  beginning  in  1775,  each  time  with 
an  instrument  of  greater  power  than  on  the  preceding,  a 
review  of  the  whole  heavens,  in  which  everything  that 
appeared  in  any  way  remarkable  was  noticed  and  if  neces- 
sary more  carefully  studied.  He  was  thus  applying  to 
astronomy  methods  comparable  with  those  of  the  naturalist 
who  aims  at  drawing  up  a  complete  list  of  the  flora  or 
fauna  of  a  country  hitherto  little  knowr 

253.  In  the  course  of  the  second  of  these  reviews,  made 
with  a  telescope  of  the  Newtonian  type,  7  feet  in  length, 
he  made  the  discovery  (March  i3th,  1781)  which  gave  him 
a  European  reputation  and  enabled  him  to  abandon  music 
as  a  profession  and  to  devote  the  whole  of  his  energies 
to  science. 

"  In  examining  the  small  stars  in  the  neighbourhood  of 
H  Geminorum  I  perceived  one  that  appeared  visibly  larger 
than  the  rest ;  being  struck  with  its  uncommon  appearance  I 
compared  it  to  H  Geminorum  and  the  small  star  in  the  quartile 
between  Auriga  and  Gemini,  and  finding  it  so  much  larger  than 
either  of  them,  I  suspected  it  to  be  a  comet." 

If  Herschel's  suspicion  had  been  correct  the  discovery 
would  have  been  of  far  less  interest  than  it  actually  was, 
for  when  the  new  body  was  further  observed  and  attempts 
were  made  to  calculate  its  path,  it  was  found  that  no 


326  A  Short  History  of  Astronomy  [Cn.  XIL 

o  dinary  cometary  orbit  would  in  any  way  fit  its  motion, 
ana  wi.hin  three  or  four  months  of  its  discovery  it  was 
recognised — first  by  Anders  Johann  Lexell  (1740-1784) — 
as  being  no  comet  but  a  new  planet,  revolving  round  the 
sun  in  a  nearly  circular  path,  at  a  distance  about  19  times 
that  of  the  earth  and  nearly  double  that  of  Saturn. 

No  new  planet  had  been  discovered  in  historic  times,  and 
Herschel's  achievement  was  therefore  absolutely  unique; 
even  the  discovery  of  satellites  inaugurated  by  Galilei 
(chapter  vi.,  §  121)  had  come  to  a  stop  nearly  a  century 
before  (1684),  when  Cassini  had  detected  his  second  pair 
of  satellites  of  Saturn  (chapter  vin.,  §  160).  Herschel 
wished  to  exercise  the  discoverer's  right  of  christening  by 
calling  the  new  planet  after  his  royal  patron  Georgium  Sidus, 
but  though  the  name  was  used  for  some  time  in  England, 
Continental  astronomers  never  accepted  it,  and  after  an 
unsuccessful  attempt  to  call  the  new  body  Herschel,  it  was 
generally  agreed  to  give  a  name  similar  to  those  of  the 
other  planets,  and  Uranus  was  proposed  and  accepted. 

Although  by  this  time  Herschel  had  published  two  or 
three  scientific  papers  and  was  probably  known  to  a  slight 
extent  in  English  scientific  circles,  the  complete  obscurity 
among  Continental  astronomers  of  the  author  of  this  memor- 
able discovery  is  curiously  illustrated  by  a  discussion  in 
the  leading  astronomical  journal  (Bode's  Astronomisches 
Jahrbucti)  as  to  the  way  to  spell  his  name,  Hertschel  being 
perhaps  the  best  and  Mersthel  the  worst  of  several  attempts. 

254.  This  obscurity  was  naturally  dissipated  by  the  dis- 
covery of  Uranus.  Distinguished  visitors  to  Bath,  among 
them  the  Astronomer  Royal  Maskelyne  (chapter  x.,  §  219), 
sought  his  acquaintance  ;  before  the  end  of  the  year  he 
was  elected  a  Fellow  of  the  Royal  Society,  in  addition  to 
receiving  one  of  its  medals,  and  in  the  following  spring  he 
was  summoned  to  Court  to  exhibit  himself,  his  telescopes, 
and  his  stars  to  George  III.  and  to  various  members  of  the 
royal  family.  As  the  outcome  of  this  visit  he  received 
from  the  King  an  appointment  as  royal  astronomer,  with 
a  salary  of  .£200  a  year. 

With  this  appointment  his  career  as  a  musician  came 
to  an  end,  and  in  August  1782  the  brother  and  sister  left 
Bath  for  good,  and  settled  first  in  a  dilapidated  house  at 


WILLIAM    HERSCHEL. 


[To  face  p. 


M  254,  255]        The  Discovery  of  Uranus :  Slough  327 

Datchet,  then,  after  a  few  months  (1785-6)  spent  at  Clay 
Hall  in  Old  Windsor,  at  Slough  in  a  house  now  known 
as  Observatory  House  and  memorable  in  Arago's  words  as 
"  le  lieu  du  monde  oil  il  a  ete  fait  le  plus  de  decouvertes." 

255.  Herschel's  modest  salary,  though  it  would  have 
sufficed  for  his  own  and  his  sister's  personal  wants,  was  of 
course  insufficient  to  meet  the  various  expenses  involved  in 
making  and  mounting  telescopes.  The  skill  which  he  had 
now  acquired  in  the  art  was,  however,  such  that  his  telescopes 
were  far  superior  to  any  others  which  were  available,  and, 
as  his  methods  were  his  own,  there  was  a  considerable 
demand  for  instruments  made  by  him.  Even  while  at 
Bath  he  had  made  and  sold  a  number,  and  for  years  after 
moving  to  the  neighbourhood  of  Windsor  he  derived  a 
considerable  income  from  this  source,  the  royal  family  and 
a  number  of  distinguished  British  and  foreign  astronomers 
being  among  his  customers. 

The  necessity  for  employing  his  valuable  time  in  this 
way  fortunately  came  to  an  end  in  1788,  when  he  married 
a  lady  with  a  considerable  fortune ;  Caroline  lived  hence- 
forward in  lodgings  close  to  her  brother,  but  worked  for 
him  with  unabated  zeal. 

By  the  end  of  1783  Herschel  had  finished  a  telescope 
20  feet  in  length  with  a  great  mirror  18  inches  in  diameter, 
and  with  this  instrument  most  of  his  best  work  was  done ; 
but  he  was  not  yet  satisfied  that  he  had  reached  the  limit 
of  what  was  possible.  During  the  last  winter  at  Bath  he 
and  his  brother  had  spent  a  great  deal  of  labour  in  an 
unsuccessful  attempt  to  construct  a  3o-foot  telescope  ;  the 
discovery  of  Uranus  and  its  consequences  prevented  the 
renewal  of  the  attempt  for  some  time,  but  in  1785  he  began 
a  4o-foot  telescope  with  a  mirror  four  feet  in  diameter,  the 
expenses  of  which  were  defrayed  by  a  special  grant  from 
the  King.  While  it  was  being  made  Herschel  tried  a  new 
form  of  construction  of  reflecting  telescopes,  suggested  by 
Lemaire  in  1732  but  never  used,  by  which  a  considerable 
gain  of  brilliancy  was  effected,  but  at  the  cost  of  some  loss 
of  distinctness.  This  Herschelian  or  front-view  construc- 
tion, as  it  is  called,  was  first  tried  with  the  2o-foot,  and  led 
to  the  discovery  (January  nth,  1787)  of  two  satellites  of 
Uranus,  Oberon  and  Titania  ;  it  was  henceforward  regularly 


328  A  Short  History  of  Astronomy  [Ca.  xn. 

employed.  After  several  mishaps  the  4o-foot  telescope 
(fig.  82)  was  successfully  constructed.  On  the  first  evening 
on  which  it  was  employed  (August  28th,  17 89)  a  sixth  satellite 
of  Saturn  (Enceladus]  was  detected,  and  on  September  iyth  a 
much  fainter  seventh  satellite  (Mimas}.  Both  satellites  were 
found  to  be  nearer  to  the  planet  than  any  of  the  five  hitherto 
discovered,  Mimas  being  the  nearer  of  the  two  (cf.  fig.  91). 

Although  for  the  detection  of  extremely  faint  objects  such 
as  these  satellites  the  great  telescope  was  unequalled,  for 
many  kinds  of  work  and  for  all  but  the  very  clearest 
evenings  a  smaller  instrument  was  as  good,  and  being  less 
unwieldy  was  much  more  used.  The  mirror  of  the  great 
telescope  deteriorated  to  some  extent,  and  after  1811, 
Herschel's  hand  being  then  no  longer  equal  to  the  delicate 
task  of  repolishing  it,  the  telescope  ceased  to  be  used 
though  it  was  left  standing  till  1839,  when  it  was  dismounted 
and  closed  up. 

256.  From  the  time  of  his  establishment  at  Slough  till 
"he  began  to  lose  his  powers  through  old  age  the  story  of 
Herschel's  life  is  little  but  a  record  of  the  work  he  did.  It 
was  his  practice  to  employ  in  observing  the  whole  of 
every  suitable  night ;  his  daylight  hours  were  devoted  to 
interpreting  his  observations  and  to  writing  the  papers  in 
which  he  embodied  his  results.  His  sister  was  nearly 
always  present  as  his  assistant  when  he  was  observing,  and 
also  did  a  good  deal  of  cataloguing,  indexing,  and  similar 
work  for  him.  After  leaving  Bath  she  also  did  some 
observing  on  her  own  account,  though  only  when  her 
brother  was  away  or  for  some  other  reason  did  not  require 
her  services  ;  she  specialised  on  comets,  and  succeeded  from 
first  to  last  in  discovering  no  less  than  eight.  To  form  any 
adequate  idea  of  the  discomfort  and  even  danger  attending 
the  nights  spent  in  observing,  it  is  necessary  to  realise  that 
the  great  telescopes  used  were  erected  in  the  open  air, 
that  for  both  the  Newtonian  and  Herschelian  forms  of 
reflectors  the  observer  has  to  be  near  the  upper  end  of  the 
telescope,  and  therefore  at  a  considerable  height  above 
the  ground.  In  the  40-foot,  for  example,  ladders  50  feet 
in  length  were  used  to  reach  the  platform  on  which  the 
observer  was  stationed.  Moreover  from  the  nature  of 
the  case  satisfactory  observations  could  not  be  taken  in  the 


256] 


Life  at  Slough 


329 


presence  either  of  the  moon  or  of  artificial  light.  It  is 
not  therefore  surprising  that  Caroline  Herschel's  journals 
contain  a  good  many  expressions  of  anxiety  for  her  brother's 


FIG.  82. — Herschel's  forty-foot  telescope. 

welfare  on  these  occasions,  and  it  is  perhaps  rather  a  matter 
of  wonder  that  so  few  serious  accidents  occurred. 

In   addition   to   doing   his   real  work  Herschel   had   to 


33°  A  Short  History  of  Astronomy  [CH.  xil. 

receive  a  large  number  of  visitors  who  came  to  Slough  out 
of  curiosity  or  genuine  scientific  interest  to  see  the  great 
man  and  his  wonderful  telescopes.  In  1801  he  went  to 
Paris,  where  he  made  Laplace's  acquaintance  and  also  saw 
Napoleon,  whose  astronomical  knowledge  he  rated  much 
below  that  of  George  III.,  while  "his  general  air  was 
something  like  affecting  to  know  more  than  he  did  know." 

In  the  spring  of  1807  he  had  a  serious  illness  ;  and  from 
that  time  onwards  his  health  remained  delicate,  and  a 
larger  proportion  of  his  time  was  in  consequence  given  to 
indoor  work.  The  last  of  the  great  series  of  papers 
presented  to  the  Royal  Society  appeared  in  1818,  when  he 
was  almost  80,  though  three  years  later  he  communicated 
a  list  of  double  stars  to  the  newly  founded  Royal  Astro- 
nomical Society.  His  last  observation  was  taken  almost  at 
the  same  time,  and  he  died  rather  more  than  a  year  after- 
wards (August  2ist,  1822),  when  he  was  nearly  84. 

He  left  one  son,  John,  who  became  an  astronomer  only 
less  distinguished  than  his  father  (chapter  xin.,  §§  306-8). 
Caroline  Herschel  after  her  beloved  brother's  death  returned 
to  Hanover,  chiefly  to  be  near  other  members  of  her  family  ; 
here  she  executed  one  important  piece  of  work  by  cataloguing 
in  a  convenient  form  her  brother's  lists  of  nebulae,  and  for 
the  remaining  26  years  of  her  long  life  her  chief  interest 
seems  to  have  been  in  the  prosperous  astronomical  career 
of  her  nephew  John. 

257.  The  incidental  references  to  Herschel's  work  that 
have  been  made  in  describing  his  career  have  shewn  him 
chiefly  as  the  constructor  of  giant  telescopes  far  surpassing 
in  power  any  that  had  hitherto  been  used,  and  as  the 
diligent  and  careful  observer  of  whatever  could  be  seen 
with  them  in  the  skies.  Sun  and  moon,  planets  and  fixed 
stars,  were  all  passed  in  review,  and  their  peculiarities  noted 
and  described.  But  this  merely  descriptive  work  was  in 
Herschel's  eyes  for  the  most  part  means  to  an  end,  for,  as 
he  said  in  1811,  "a  knowledge  of  the  construction  of  the 
heavens  has  always  been  the  ultimate  object  of  my 
observations." 

Astronomy  had  for  many  centuries  been  concerned  almost 
wholly  with  the  positions  of  the  various  heavenly  bodies 
on  the  celestial  sphere,  that  is  with  their  directions. 


§25?]  HerscheVs  Astronomical  Programme  331 

Coppernicus  and  his  successors  had  found  that  the  apparent 
motions  on  the  celestial  sphere  of  the  members  of  the  solar 
system  could  only  be  satisfactorily  explained  by  taking 
into  account  their  actual  motions  in  space,  so  that  the 
solar  system  came  to  be  effectively  regarded  as  consisting 
of  bodies  at  different  distances  from  the  earth  and  separated 
from  one  another  by  so  many  miles.  But  with  the  fixed 
stars  the  case  was  quite  different :  for,  with  the  unimportant 
exception  of  the  proper  motions  of  a  few  stars  (chapter  x., 
§  203),  all  their  known  apparent  motions  were  explicable  as 
the  result  of  the  motion  of  the  earth  ;  and  the  relative  or  actual 
distances  of  the  stars  scarcely  entered  into  consideration. 
Although  the  belief  in  a  real  celestial  sphere  to  which  the 
stars  were  attached  scarcely  survived  the  onslaughts  of 
Tycho  Brahe  and  Galilei,  and  any  astronomer  of  note 
in  the  latter  part  of  the  iyth  or  in  the  i8th  century  would, 
if  asked,  hive  unhesitatingly  declared  the  stars  to  be  at 
different  distances  from  the  earth,  this  was  in  effect  a 
mere  pious  opinion  which  had  no  appreciable  effect  on 
astronomical  work. 

The  geometrical  conception  of  the  stars  as  represented 
by  points  on  a  celestial  sphere  was  in  fact  sufficient  for 
ordinary  astronomical  purposes,  and  the  attention  of  great 
observing  astronomers  such  as  Flamsteed,  Bradley,  and 
Lacaille  was  directed  almost  entirely  towards  ascertaining 
the  positions  of  these  points  with  the  utmost  accuracy  or 
towards  observing  the  motions  of  the  solar  system.  More- 
over the  group  of  problems  which  Newton's  work  suggested 
naturally  concentrated  the  attention  of  eighteenth-century 
astronomers  on  the  solar  system,  though  even  from  this 
point  of  view  the  construction  of  star  catalogues  had  con- 
siderable value  as  providing  reference  points  which  could 
be  used  for  fixing  the  positions  of  the  members  of  the  solar 
system. 

Almost  the  only  exception  to  this  general  tendency 
consisted  in  the  attempts — hitherto  unsuccessful — to  find 
the  parallaxes  and  hence  the  distances  of  some  of  the 
fixed  stars,  a  problem  which,  though  originally  suggested 
by  the  Coppernican  controversy,  had  been  recognised  as 
possessing  great  intrinsic  interes^. 

Herschel  therefore  struck  out  an  entirely  new  path  when 


532  A  Short  History  of  Astronomy  [CH.  xn. 

he  began  to  study  the  sidereal  system  per  se  and  the 
mutual  relations  of  its  members.  From  this  point  of  view 
the  sun,  with  its  attendant  planets,  became  one  of  an 
innumerable  host  of  stars,  which  happened  to  have  received 
a  fictitious  importance  from  the  accident  that  we  inhabited 
one  member  of  its  system. 

258.  A  complete  knowledge  of  the  positions  in  space 
of  the  stars  would  of  course  follow  from  the  measurement 
of  the  parallax  (chapter  vi.,  §  129  and  chapter  x.,  §  207)  of 
each.  The  failure  of  such  astronomers  as  Bradley  to  get  the 
parallax  of  any  one  star  was  enough  to  shew  the  hopelessness 
of  this  general  undertaking,  and,  although  Herschel  did  make 
an  attack  on  the  parallax  problem  (§  263),  he  saw  that  the 
question  of  stellar  distribution  in  space,  if  to  be  answered 
at  all,  required  some  simpler  if  less  reliable  method  capable 
of  application  on  a  large  scale. 

Accordingly  he  devised  (1784)  his  method  of  star- 
gauging.  The  most  superficial  view  of  the  sky  shews  that 
the  stars  visible  to  the  naked  eye  are  very  unequally  dis- 
tributed on  the  celestial  sphere ;  the  same  is  true  when 
the  fainter  stars  visible  in  a  telescope  are  taken  into  account. 
If  two  portions  of  the  sky  of  the  same  apparent  or  angular 
magnitude  are  compared,  it  may  be  found  that  the  first 
contains  many  times  as  many  stars  as  the  second.  If  we 
realise  that  the  stars  are  not  actually  on  a  sphere  but  are 
scattered  through  space  at  different  distances  from  us, 
we  can  explain  this  inequality  of  distribution  on  the  sky 
as  due  to  either  a  real  inequality  of  distribution  in  space, 
or  to  a  difference  in  the  distance  to  which  the  sidereal 
system  extends  in  the  directions  in  which  the  two  sets  of 
stars  lie.  The  first  region  on  the  sky  may  correspond  to 
a  region  of  space  in  which  the  stars  are  really  clustered 
together,  or  may  represent  a  direction  in  which  the  sidereal 
system  extends  to  a  greater  distance,  so  that  the  accumula- 
tion of  layer  after  layer  of  stars  lying  behind  one  another 
produces  the  apparent  density  of  distribution.  In  the  same 
way,  if  we  are  standing  in  a  wood  and  the  wood  appears 
less  thick  in  one  direction  than  in  another,  it  may  be 
because  the  trees  are  really  more  thinly  planted  there  or 
because  in  that  direction  the  edge  of  the  wood  is  nearer. 

In  the  absence  of  any  a  priori  knowledge  of  the  actual 


5  258J  Star-gauging  333 

clustering  of  the  stars  in  space,  Herschel  chose  the  former 
of  these  two  hypotheses;  that  is,  he  treated  the  apparent 
density  of  the  stars  on  any  particular  part  of  the  sky  as 
a  measure  of  the  depth  to  which  the  sidereal  systems 
extended  in  that  direction,  and  interpreted  from  this  point 
of  view  the  results  of  a  vast  series  of  observations.  He 
used  a  2o-foot  telescope  so  arranged  that  he  could  see 
with  it  a  circular  portion  of  the  sky  15'  in  diameter  (one- 
quarter  the  area  of  the  sun  or  full  moon),  turned  the  telescope 
to  different  parts  of  the  sky,  and  counted  the  stars  visible 
in  each  case.  To  avoid  accidental  irregularities  he  usually 
took  the  average  of  several  neighbouring  fields,  and  published 
in  1785  the  results  of  gauges  thus  made  in  683*  regions, 


FIG.  83. — Section  of  the  sidereal  system.     From  Herschel's  paper  in 
the  Philosophical  Transactions. 

while  he  subsequently  added  400  others  which  he  did  not 
think  it  necessary  to  publish.  Whereas  in  some  parts  of 
the  sky  he  could  see  on  an  average  only  one  star  at  a  time, 
in  others  nearly  600  were  visible,  and  he  estimated  that 
on  one  occasion  about  116,000  stars  passed  through  the 
field  of  view  of  his  telescope  in  a  quarter  of  an  hour. 
The  general  result  was,  as  rough  naked-eye  observation 
suggests,  that  stars  are  most  plentiful  in  and  near  the 
Milky  Way  and  least  so  in  the  parts  of  the  sky  most  remote 
from  it.  Now  the  Milky  Way  forms  on  the  sky  an  ill- 
defined  band  never  deviating  much  from  a  great  circle 
(sometimes  called  the  galactic  circle) ;  so  that  on  Herschel's 
hypothesis  the  space  occupied  by  the  stars  is  shaped 
roughly  like  a  disc  or  grindstone,  of  which  according  to 

*  In  his  paper  of  1817  Herschel  gives  the  number  as  863,  but  a 
reference  to  the  original  paper  of  1785  shews  that  this  must  be  a 
printer's  error. 


J34  A  Short  History  of  Astronomy  [CH.  xii. 

his  figures  the  diameter  is  about  five  times  the  thickness. 
Further,  the  Milky  Way  is  during  part  of  its  length  divided 
into  two  branches,  the  space  between  the  two  branches 
being  comparatively  free  of  stars.  Corresponding  to  this 
subdivision  there  has  therefore  to  be  assumed  a  cleft  in 
the  "grindstone." 

This  "grindstone"  theory  of  the  universe  had  been 
suggested  in  1750  by  Thomas  Wright  (1711-1786)  in  his 
Theory  of  the  Universe^  and  again  by  Kant  five  years  later; 
but  neither  had  attempted,  like  Herschel,  to  collect  numerical 
data  and  to  work  out  consistently  and  in  detail  the  conse- 
quences of  the  fundamental  hypothesis. 

That  the  assumption  of  uniform  distribution  of  stars  in 
space  could  not  be  true  in  detail  was  evident  to  Herschel 
from  the  beginning.  A  star  cluster,  for  example,  in  which 
many  thousands  of  faint  stars  are  collected  together  in  a 
very  small  space  on  the  sky,  would  have  to  be  interpreted 
as  representing  a  long  projection  or  spike  full  of  stars, 
extending  far  beyond  the  limits  of  the  adjoining  portions  of 
the  sidereal  system,  and  pointing  directly  away  from  the 
position  occupied  by  the  solar  system.  In  the  same  way 
certain  regions  in  the  sky  which  are  found  to  be  bare  of 
stars  would  have  to  be  regarded  as  tunnels  through  the 
stellar  system.  That  even  one  or  two  such  spikes  or  tunnels 
should  exist  would  be  improbable  enough,  but  as  star 
clusters  were  known  in  considerable  numbers  before  Her- 
schel began  his  work,  and  were  discovered  by  him  in 
hundreds,  it  was  impossible  to  explain  their  existence  on 
this  hypothesis,  and  it  became  necessary  to  assume  that  a 
star  cluster  occupied  a  region  of  space  in  which  stars  were 
really  closer  together  than  elsewhere. 

Moreover  further  study  of  the  arrangement  of  the  stars, 
particularly  of  those  in  the  Milky  Way,  led  Herschel  gradu- 
ally to  the  belief  that  his  original  assumption  was  a  wider 
departure  from  the  truth  than  he  had  at  first  supposed  ; 
and  in  1811,  nearly  30  years  after  he  had  begun  star- 
gauging,  he  admitted  a  definite  change  of  opinion : — 

"  I  must  freely  confess  that  by  continuing  my  sweeps  of  the 
heavens  my  opinion  of  the  arrangement  of  the  stars  .  .  .  has 
undergone  a  gradual  change.  .  .  .  For  instance,  an  equal  scattering 


$  25sj  The  Structure  of  the  Sidereal  System  335 

of  the  stars  may  be  admitted  in  certain  calculations  ;  bv.t  when 
we  examine  the  Milky  Way,  or  the  closely  compressed  clusters 
of  stars  of  which  my  catalogues  have  recorded  so  many  instances, 
this  supposed  equality  of  scattering  must  be  given  up." 

The  method  of  star-gauging  was  intended  primarily  to  give 
information  as  to  the  limits  of  the  sidereal  system — or  the 
visible  portions  of  it.  Side  by  side  with  this  method  Herschel 
constantly  made  use  of  the  brightness  of  a  star  as  a  probable 
test  of  nearness.  \IfjUvo  stars  give  out  actually  the  same 
amount  of  light,  men  that  one  which  is  nearer  to  us  will 
appear  the  brighter  ;  and  on  the  assumption  that  no  light 
is  absorbed  or  stopped  in  its  passage  though  gp-^,  «*"» 
apparent  brightness  of  the  two  stars  will  be  inversely  n<;  thp 
square  of  their  respective  distances.  Hence,  if  we  receive 
mhe  tlmCS  as  much  light  from  one  star  as  from  another, 
and  if  it  is  assumed  that  this  difference  is  merely  due  to 
difference  of  distance,  then  the  first  star  is  three  times  as 
far  off  as  the  second,  and  so  on.  « 

That  the  stars  as  a  whole  give  out  the  same  amount  of  fl 
light,  so  that  the  difference  in  their  apparent  brightness  is  I 
due  to  distance  only,  is  an  assumption  of  the  same  general./ 
character  as  that  of  equal  distribution.     There  must  neces- 
sarily be  many  exceptions,  but,  in  default  of  more  exact 
knowledge,  it  affords  a  rough-and-ready  method  of  estimating 
with  some  degree  of  probability  relative  distances  of  stars. 

To  apply  this  method  it  was  necessary  to  have  some 
means  of  comparing  the  amount  of  light  received  from 
different  stars.  This  Herschel  effected  by  using  telescopes  of 
different  sizes.  ^sILthe  same  star  is 

ing  telescopes  of  the  same  construction  but  of  different 
sizes,  then  the  light  transmitted  by  the  telescope  to  the  eye 
is  proportional  to  the  area  of  the  mirror  which  collects  the 
light,  and  hence  to  the  -sq^aje-of  the  Diameter  .of  the 
HeilCt!  the1  apparent  brightness  of  a  staT¥s~^ewed^troug 
a  telescope  is  proportional  on  the  one  hand  to  the  inverse 
square  of  the  distance,  and  on  the  other  to  the  square  of 
the  diameter  of  the  mirror  of  the  telescope  ;  hence  the 
distance  of  the  star  is,  as  it  were,  exactly  counterbalanced  by 
the  diameter  of  the  mirror  of  the  telescope.  For  example, 
if  one  star  viewed  in  a  telescope  with  an  eight-inch  mirror 
and  another  viewed  in  the  great  telescope  with  a  four-foot 


336  A  Short  History  of  Astronomy  [CH.  xn. 

mirror  appear  equally  bright,  then  the  second  star  is — on 
the  fundamental  assumption — six  times  as  far  off. 

In  the  same  way  the  size  of  the  mirror  necessary  to  make 
a  star  just  visible  was  used  by  Herschel  as  a  measure  of 
the  distance  of  the  star,  and  it  was  in  this  sense  that  he 
constantly  referred  to  the  "  space-penetrating  power  "  of  his 
telescope.  On  this  assumption  he  estimated  the  faintest 
stars  visible  to  the  naked  eye  to  be  about  twelve  times  as 
remote  as  one  of  the  brightest  stars,  such  as  Arcturus,  while 
Arcturus  if  removed  to  900  times  its  present  distance  would 
just  be  visible  in  the  2o-foot  telescope  which  he  commonly 
used,  and  the  4o-foot  would  penetrate  about  twice  as  far 
into  space. 

Towards  the  end  of  his  life  (1817)  Herschel  made  an 
attempt  to  compare  statistically  his  two  assumptions  of 
uniform  distribution  in  space  and  of  uniform  actual  bright- 
ness, by  counting  the  number  of  stars  of  each  degree  of 
apparent  brightness  and  comparing  them  with  the  numbers 
that  would  result  from  uniform  distribution  in  space  if 
apparent  brightness  depended  only  on  distance.  The 
inquiry  only  extended  as  far  as  stars  visible  to  the  naked 
eye  and  to  the  brighter  of  the  telescopic  stars,  and  indicated 
the  existence  of  an  excess  of  the  fainter  stars  of  these 
classes,  so  that  either  these  stars  are  more  closely  packed 
in  space  than  the  brighter  ones,  or  they  are  in  reality  smaller 
or  less  luminous  than  the  others;  but  no  definite  con- 
clusions as  to  the  arrangement  of  the  stars  were  drawn. 

259.  Intimately  connected  with  the  structure  of  the  sidereal 
system  was  the  question  of  the  distribution  and  nature  of 
nebulae  (cf.  figs.  100,  102,  facing  pp.  397,  400)  and  star 
clusters  (cf.  fig.  104,  facing  p.  405).  When  Herschel  began 
his  work  rather  more  than  100  such  bodies  were  known, 
which  had  been  discovered  for  the  most  part  by  the  French 
observers  Lacaille  (chapter  x.,  §  223)  and  Charles  Messier 
(1730-1817).  Messier  maybe  said  to  have  been  a  comet- 
hunter  by  profession ;  finding  himself  liable  to  mistake 
nebulae  for  comets,  he  put  on  record  (1781)  the  positions 
of  103  of  the  former.  Herschel's  discoveries — carried  out 
much  more  systematically  and  with  more  powerful  instru- 
mental appliances — were  on  a  far  larger  scale.  In  1786 
he  presented  to  the  Royal  Society  a  catalogue  of  1,000 


$$  259,  26  ]  Nebulae  and  Star  Clusters  337 

new  nebulae  and  clusters,  three  years  later  a  second  cata- 
logue of  the  same  extent,  and  in  1802  a  third  comprising 
500.  Each  nebula  was  carefully  observed,  its  general 
appearance  as  well  as  its  position  being  noted  and  described, 
and  to  obtain  a  general  idea  of  the  distribution  of  nebulae 
on  the  sky  the  positions  were  marked  on  a  star  map. 
The  differences  in  brightness  and  in  apparent  structure  led 
to  a  division  into  eight  classes  ;  and  at  quite  an  early  stage 
of  his  work  (1786)  he  gave  a  graphic  account  of  the  extra- 
ordinary varieties  in  form  which  he  had  noted : — 

"  I  have  seen  double  and  treble  nebulae,  variously  arranged  ; 
large  ones  with  small,  seeming  attendants;  narrow  but  much 
extended,  lucid  nebulae  or  bright  dashes  ;  some  of  the  shape 
of  a  fan,  resembling  an  electric  brush,  issuing  from  a  lucid 
point;  others  of  the  cometic  shape,  with  a  seeming  nucleus 
in  the  center ;  or  like  cloudy  stars,  surrounded  with  a  nebulous 
atmosphere  ;  a  different  sort  again  contain  a  nebulosity  of  the 
milky  kind,  like  that  wonderful  inexplicable  phenomenon  about 
6  Orionis ;  while  others  shine  with  a  fainter  mottled  kind 
of  light,  which  denotes  their  being  resolvable  into  stars." 

260.  But  much  the  most  interesting  problem  in  classifica- 
tion was  that  of  the  relation  between  nebulae  and  star  clusters. 
The  Pleiades,  for  example,  appear  to  ordinary  eyes  as  a 
group  of  six  stars  close  together,  but  many  short-sighted 
people  only  see  there  a  portion  of  the  sky  which  is  a  little 
brighter  than  the  adjacent  region ;  again,  the  nebulous 
patch  of  light,  as  it  appears  to  the  ordinary  eye,  known  as 
Praesepe  (in  the  Crab),  is  resolved  by  the  smallest  telescope 
into  a  cluster  of  faint  stars.  In  the  same  way  there  are 
other  objects  which  in  a  small  telescope  appear  cloudy  or 
nebulous,  but  viewed  in  an  instrument  of  greater  power  are 
seen  to  be  star  clusters.  In  particular  Herschel  found  that 
many  objects  which  to  Messier  were  purely  nebulous 
appeared  in  his  own  great  telescopes  to  be  undoubted 
clusters,  though  others  still  remained  nebulous.  Thus  in 
his  own  words  : — 

"  Nebulae  can  be  selected  so  that  an  insensible  gradation 
shall  take  place  from  a  coarse  cluster  like  the  Pleiades  down 
to  a  milky  nebulosity  like  that  in  Orion,  every  intermediate  step 
being  represented." 

A  22 


338  A  Short  History  of  Astronomy  [CH.  xi.i 

These  facts  suggested  obviously  the  inference  that  the 
difference  between  nebulae  and  star  clusters  was  merely  a 
question  of  the  power  of  the  telescope  employed,  and  accord- 
ingly Herschel's  next  sentence  is  : — 

4<  This  tends  to  confirm  the  hypothesis  that  all  are  composed 
of  stars  more  or  less  remote." 

The  idea  was  not  new,  having  at  any  rate  been  suggested, 
rather  on  speculative  than  on  scientific  grounds,  in  1755 
by  Kant,  who  had  further  suggested  that  a  single  nebula 
or  star  cluster  is  an  assemblage  of  stars  comparable  in 
magnitude  and  structure  with  the  whole  of  those  which 
constitute  the  Milky  Way  and  the  other  separate  stars  which 
we  see.  From  this  point  of  view  the  sun  is  one  star  in  a 
cluster,  and  every  nebula  which  we  see  is  a  system  of  the 
same  order.  This  "  island  universe  "  theory  of  nebulae,  as 
it  has  been  called,  was  also  at  first  accepted  by  Herschel, 
so  that  he  was  able  once  to  tell  Miss  Burney  that  he  had 
discovered  1,500  new  universes. 

Herschel,  however,  was  one  of  those  investigators  who 
hold  theories  lightly,  and  as  early  as  1791  further  observa- 
tion had  convinced  him  that  these  views  were  untenable, 
and  that  some  nebulae  at  least  were  essentially  distinct  from 
star  clusters.  The  particular  object  which  he  quotes  in 
support  of  his  change  of  view  was  a  certain  nebulous  star — • 
that  is,  a  body  resembling  an  ordinary  star  but  surrounded 
by  a  circular  halo  gradually  diminishing  in  brightness. 

"Cast  your  eye,"  he  says,  "on  this  cloudy -star,  and  the 
result  will  be  no  less  decisive.  .  .  .  Your  judgement,  I  may 
venture  to  say,  will  be,  that  the  nebulosity  about  the  star  is  not 
of  a  starry  nature" 

If  the  nebulosity  were  due  to  an  aggregate  of  stars  so 
far  off  as  to  be  separately  indistinguishable,  then  the  central 
body  would  have  to  be  a  star  of  almost  incomparably  greater 
dimensions  than  an  ordinary  star;  if,  on  the  other  hand, 
the  central  body  were  of  dimensions  comparable  with  those 
of  an  ordinary  star,  the  nebulosity  must  be  due  to  some- 
thing other  than  a  star  cluster.  In  either  case  the  object 
presented  features  markedly  different  from  those  of  a  star 
cluster  of  the  recognised  kind  ;  and  of  the  two  alternative 


§  26i]  Nebulae  and  Star  Clusters  339 

explanations  Herschel  chose  the  latter,  considering  the 
nebulosity  to  be  "  a  shining  fluid,  of  a  nature  totally  un- 
known to  us."  One  exception  to  his  earlier  views  being 
thus  admitted,  others  naturally  followed  by  analogy,  and 
henceforward  he  recognised  nebulae  of  the  "shining  fluid" 
class  as  essentially  different  from  star  clusters,  though  it 
might  be  impossible  in  many  cases  to  say  to  which  class 
a  particular  body  belonged. 

The  evidence  accumulated  by  Herschel  as  to  the  distri- 
bution of  nebulae  also  shewed  that,  whatever  their  nature, 
they  could  not  be  independent  of  the  general  sidereal 
system,  as  on  the  "  island  universe  "  theory.  In  the  first 
place  observation  soon  shewed  him  that  an  individual  nebula 
or  cluster  was  usually  surrounded  by  a  region  of  the  sky 
comparatively  free  from  stars ;  this  was  so  commonly  the 
case  that  it  became  his  habit  while  sweeping  for  nebulae, 
after  such  a  bare  region  had  passed  through  the  field  of 
his  telescope,  to  warn  his  sister  to  be  ready  to  take  down 
observations  of  nebulae.  Moreover,  as  the  position  of  a 
large  number  of  nebulae  came  to  be  known  and  charted, 
it  was  seen  that,  whereas  clusters  were  common  near  the 
Milky  Way,  nebulae  which  appeared  ii. capable  of  resolution 
into  clusters  were  scarce  there,  and  shewed  on  the  contrary 
a  decided  tendency  to  be  crowded  together  in  the  regions 
of  the  sky  most  remote  from  the  Milky  Way — that  is,  round 
the  poles  of  the  galactic  circle  (§  258).  If  nebulae  were 
external  systems,  there  would  of  course  be  no  reason  why 
their  distribution  on  the  sky  should  shew  any  connection 
either  with  the  scarcity  of  stars  generally  or  with  the  position 
of  the  Milky  Way. 

It  is,  however,  rather  remarkable  that  Herschel  did  not 
in  this  respect  fully  appreciate  the  consequences  of  his 
own  observations,  and  up  to  the  end  of  his  life  seems 
to  have  considered  that  some  nebulae  and  clusters  were 
external  "  universes,"  though  many  were  part  of  our  own 
system. 

261.  As  early  as  1789  Herschel  had  thrown  out  the 
idea  that  the  different  kinds  of  nebulae  and  clusters  were 
objects  of  the  same  kind  at  different  stages  of  develop- 
ment, some  "  clustering  power  "  being  at  work  converting 
a  diffused  nebula  into  a  brighter  and  more  condensed 


34°  A  Short  History  of  Astronomy  [CH.  xil. 

body ;   so  that  condensation  could  be  regarded  as  a  sign 
of  "  age."     And  he  goes  on  :— 

"  This  method  of  viewing  the  heavens  seems  to  throw  them 
into  a  new  kind  of  light.  They  are  now  seen  to  resemble  a  luxu- 
riant garden,  which  contains  the  greatest  variety  of  productions,  in 
different  flourishing  beds  ;  and  one  advantage  we  may  at  least 
reap  from  it  is,  that  we  can,  as  it  were,  extend  the  range  of 
our  experience  to  an  immense  duration.  For,  to  continue  the 
simile  I  have  borrowed  from  the  vegetable  kingdom,  is  it  not 
almost  the  same  thing,  whether  we  live  successively  to  witness 
the  germination,  blooming,  foliage,  fecundity,  fading,  withering 
and  corruption  of  a  plant,  or  whether  a  vast  number  of 
specimens,  selected  from  every  stage  through  which  the  plant 
passes  in  the  course  of  its  existence,  be  brought  at  once  to 
our  view  ?  " 

His  change  of  opinion  in  1791  as  to  the  nature  of  nebulae 
led  to  a  corresponding  modification  of  his  views  of  this 
process  of  condensation.  Of  the  star  already  referred  to 
(§  260)  he  remarked  that  its  nebulous  envelope  "  was  more 
fit  to  produce  a  star  by  its  condensation  than  to  depend  upon 
the  star  for  its  existence."  In  1811  and  1814  he  published 
a  complete  theory  of  a  possible  process  whereby  the  shining 
fluid  constituting  a  diffused  nebula  might  gradually  con- 
dense— the  denser  portions  of  it  being  centres  of  attraction — 
first  into  a  denser  nebula  or  compressed  star  cluster,  then 
into  one  or  more  nebulous  stars,  lastly  into  a  single  star 
or  group  of  stars.  Every  supposed  stage  in  this  process 
was  abundantly  illustrated  from  the  records  of  actual  nebulae 
and  clusters  which  he  had  observed. 

In  the  latter  paper  he  also  for  the  first  time  recognised 
that  the  clusters  in  and  near  the  Milky  Way  really  belonged 
to  it,  and  were  not  independent  systems  that  happened  to 
lie  in  the  same  direction  as  seen  by  us. 

262.  On  another  allied  point  Herschel  also  changed  his 
mind  towards  the  end  of  his  life.  When  he  first  used  his 
great  2O-foot  telescope  to  explore  the  Milky  Way,  he  thought 
that  he  had  succeeded  in  completely  resolving  its  faint 
cloudy  light  into  component  stars,  and  had  thus  penetrated 
to  the  end  of  the  Milky  Way  ;  but  afterwards  he  was  con- 
vinced that  this  was  not  the  case,  but  that  there  remained 
cloudy  portions  which — whether  on  account  of  their  remote- 


;$  262,  a6j]    Condensation  of  Nebulae :  Double  Stars  341 

ness  or  for   other  reasons — his  telescopes  were  unable  to 
resolve  into  stars  (cf.  fig.  104,  facing  p.  405). 

In  both  these  respects  therefore  the  structure  of  the 
Milky  Way  appeared  to  him  finally  less  simple  than  at 
first. 

^^j0ne  of  the  most  notable  of  Herschel's  discoveries 
was  a  bye-product  of  an  inquiry  of  an  entirely  different 
character.  Just  as  Bradley  in  trying  to  find  the  parallax  of 
a  star  discovered  aberration  and  nutation  (chapter  x.,  §  207), 
so  also  the  same  problem  in  Herschel's  hands  led  to  the 
d:scovery  of  double  stars.  He  proposed  to  employ  Galilei's 
differential  or  double-star  method  (chapter  vi.,  §  129),  in 
which  the  minute  shift  of  a  star's  position,  due  to  the  earth's 
motion  round  the  sun,  is  to  be  detected  not  by  measuring 
its  angular  distance  from  standard  points  on  the  celestial 
sphere  such  as  the  pole  or  the  zenith,  but  by  observing  the 
variations  in  its  distance  from  some  star  close  to  it,  whic'i 
from  its  faintness  or  for  some  other  reason  might  be 
supposed  much  further  off  and  therefore  less  affected  by 
the  earth's  motion. 

With  this  object  in  view  Herschel  set  to  work  to  find 
pairs  of  stars  close  enough  together  to  be  suitable  for  his 
purpose,  and,  with  his  usual  eagerness  to  see  and  to  record 
all  that  could  be  seen,  gathered  in  an  extensive  harvest 
of  such  objects.  The  limit  of  distance  between  the  two 
members  of  a  pair  beyond  which  he  did  not  think  it  worth 
while  to  go  was  2',  an  interval  imperceptible  to  the  naked 
eye  except  in  cases  of  quite  abnormally  acute  sight.  In 
other  words,  the  two  stars — even  if  bright  enough  to  be 
visible — would  always  appear  as  one  to  the  ordinary  eye. 
A  first  catalogue  of  such  pairs,  each  forming  what  may 
be  called  a  double  star,  was  published  early  in  1782  and 
contained  269,  of  which  227  were  new  discoveries;  a  second 
catalogue  of  434  was  presented  to  the  Royal  Society  at  the 
end  of  1784;  and  his  last  paper,  sent  to  the  Royal  Astro- 
nomical Society  in  1821  and  published  in  the  first  volume 
of  its  memoirs,  contained  a  list  of  145  more.  In  addition  to 
the  position  of  each  double  star  the  angular  distance  between 
the  two  members,  the  direction  of  the  line  joining  them, 
and  the  brightness  of  each  were  noted.  In  some  cases  also 
curious  contrasts  in  the  colour  of  the  two  components  were 


342  A  Short  History  of  Astronomy  [Cn.  xn. 

observed.  There  were  also  not  a  few  cases  in  which  not 
merely  two,  but  three,  four,  or  more  stars  were  found  close 
enough  to  one  another  to  be  reckoned  as  forming  a  multiple 
star. 

Herschel  had  begun  with  the  idea  that  a  double  star 
was  due  to  a  merely  accidental  coincidence  in  the  direction 
of  two  stars  which  had  no  connection  with  one  another  and 
one  of  which  might  be  many  times  as  remote  as  the  other. 
It  had,  however,  been  pointed  out  by  Michell  (chapter  x., 
§  219),  as  early  as  1767,  that  even  the  few  double  stars 
then  known  afforded  examples  of  coincidences  which  were 
very  improbable  as  the  result  of  mere  random  distribution 
of  stars.  A  special  case  may  be  taken,  to  make  the  argu- 
ment clearer,  though  Michell's  actual  reasoning  was  not 
put  into  a  numerical  form.  The  bright  star  Castor  (in  the 
Twins)  had  for  some  time  been  known  to  consist  of  two 
stars,  a  and  /?,  rather  less  than  5"  apart.  Altogether  there 
are  about  50  stars  of  the  same  order  of  brightness  as  a,  and 
400  like  ft.  Neither  set  of  stars  shews  any  particular 
tendency  to  be  distributed  in  any  special  way  over  the 
celestial  sphere.  So  that  the  question  of  probabilities 
becomes  :  if  there  are  50  stars  of  one  sort  and  400  of  anothu  r 
distributed  at  random  over  the  whole  celestial  sphere,  the 
two  distributions  having  no  connection  with  one  another, 
what  is  the  chance  that  one  of  the  first  set  of  stars  should. 
be  within  5"  of  one  of  the  second  set  ?  The  chance  is 
about  the  same  as  that,  if  50  grains  of  wheat  and  400  of 
barley  are  scattered  at  random  in  a  field  of  i  oo  acres,  one 
grain  of  wheat  should  be  found  within  half  an  inch  of  a 
grain  of  barley.  The  odds  against  such  a  possibility  are 
clearly  very  great  and  can  be  shewn  to  be  more  than 
300,000  to  one.  These  are  the  odds  against  the  existence 
— without  some  real  connection  between  the  members — of 
a  single  double  star  like  Castor;  but  when  Herschel  began 
to  discover  double  stars  by  the  hundred  the  improbability 
was  enormously  increased.  In  his  first  paper  Herschel 
gave  as  his  opinion  that  "  it  is  much  too  soon  to  form  any 
theories  of  small  stars  revolving  round  large  ones,"  a  remark 
shewing  that  the  idea  had  been  considered;  and  in  1784 
Michell  returned  to  the  subject,  and  expressed  the  opinirn 
that  the  odds  in  favour  of  a  physical  relation  between  the 


$  264]  Double  Stars  343 

members  of  Herschel's  newly  discovered  double  stars  were 
"  beyond  arithmetic." 

264.  Twenty  years  after  the  publication  of  his  first 
catalogue  Herschel  was  of  Michell's  opinion,  but  was 
now  able  to  support  it  by  evidence  of  an  entirely  novel 
and  much  more  direct  character.  A  series  of  observations 
of  Castor,  presented  in  two  papers  published  in  the  Philo- 
sophical Transactions  in  1803  and  1804,  which  were  fortu- 
nately supplemented  by  an  observation  of  Bradley's  in 
1759,  had  shewn  a  progressive  alteration  in  the  direction 
of  the  line  joining  its  two  components,  of  such  a  character 
as  to  leave  no  doubt  that  the  two  stars  were  revolving 
round  one  another ;  and  there  were  five  other  cases  in 
which  a  similar  motion  was  observed.  In  these  six  cases 
it  was  thus  shewn  that  the  double  star  was  really  formed  by 
a  connected  pair  of  stars  near  enough  to  influence  one 
another's  motion.  A  double  star  of  this  kind  is  called  a 
binary  star  or  a  physical  double  star,  as  distinguished  from 
a  merely  optical  double  star,  the  two  members  of  which  have 
no  connection  with  one  another.  In  three  cases,  including 
Castor,  the  observations  were  enough  to  enable  the  period 
of  a  complete  revolution  of  one  star  round  another,  assumed 
to  go  on  at  a  uniform  rate,  to  be  at  any  rate  roughly 
estimated,  the  results  given  by  Herschel  being  342  years 
for  Castor,*  375  and  1,200  years  for  the  other  two.  It  was 
an  obvious  inference  that  the  motion  of  revolution  observed 
in  a  binary  star  was  due  to  the  mutual  gravitation  of  its 
members,  though  Herschel's  data  were  not  enough  to 
determine  with  any  precision  the  law  of  the  motion,  and 
it  was  not  till  five  years  after  his  death  that  the  first  attempt 
was  made  to  shew  that  the  orbit  of  a  binary  star  was  such 
as  would  follow  from,  or  at  any  rate  would  be  consistent 
with,  the  mutual  gravitation  of  its  members  (chapter  xni., 
§  309  :  cf.  also  fig.  101).  This  may  be  regarded  as  the  first 
direct  evidence  of  the  extension  of  the  law  of  gravitation  to 
regions  outside  the  solar  system. 

Although  only  a  few  double  stars  were  thus  definitely 
shewn  to  be  binary,  there  was  no  reason  why  many  others 

*  The  motion  of  Castor  has  become  slower  since  Herschel's  time, 
and  the  present  estimate  of  the  period  is  about  1,000  years,  but  it 
is  by  no  means  certain. 


344  A  Short  History  of  Astronomy  [CH.  xii. 

should  not  be  so  also,  their  motion  not  having  been  rapid 
enough  to  be  clearly  noticeable  during  the  quarter  of  a 
century  or  so  over  which  Herschel's  observations  extended ; 
and  this  probability  entirely  destroyed  the  utility  of  double 
stars  for  the  particular  purpose  for  which  Herschel  had 
originally  sought  them.  For  if  a  double  star  is  binary, 
then  the  two  members  are  approximately  at  the  same 
distance  from  the  earth  and  therefore  equally  affected  by 
the  earth's  motion,  whereas  for  the  purpose  of  finding  the 
parallax  it  is  essential  that  one  should  be  much  more 
remote  than  the  other.  But  the  discovery  which  he  had 
made  appeared  to  him  far  more  interesting  than  that  which 
he  had  attempted  but  failed  to  make  ;  in  his  own  picturesque 
language,  he  had,  like  Saul,  gone  out  to  seek  his  father's 
asses  and  had  found  a  kingdom. 

265.  It  had  been  known  since  Halley's  time  (chapter  x., 
§  203)  that  certain  stars  had  proper  motions  on  the  celestial 
sphere,  relative  to  the  general  body  of  stars.  The  conviction, 
that  had  been  gradually  strengthening  among  astronomers, 
that  the  sun  is  only  one  of  the  fixed  stars,  suggested  the 
possibility  that  the  sun,  like  other  stars,  might  have  a 
motion  in  space.  Thomas  Wright,  Lambert,  and  others 
had  speculated  on  the  subject,  and  Tobias  Mayer  (chapter  x., 
§§  225-6)  had  shewn  how  to  look  for  such  a  motion. 

If  a  single  star  appears  to  move,  then  by  the  principle  of 
relative  motion  (chapter  iv.,  §  77)  this  may  be  explained 
equally  well  by  a  motion  of  the  star  or  by  a  motion  of  the 
observer,  or  by  a  combination  of  the  two ;  and  since  in  this 
problem  the  internal  motions  of  the  solar  system  may  be 
ignored,  this  motion  of  the  observer  may  be  identified  with 
that  of  the  sun.  When  the  proper  motions  of  several  stars 
are  observed,  a  motion  of  the  sun  only  is  in  general  inade- 
quate to  explain  them,  but  they  may  be  regarded  as  due 
either  solely  to  the  motions  in  space  of  the  stars  or  to 
combinations  of  these  with  some  motion  of  the  sun.  If 
now  the  stars  be  regarded  as  motionless  and  the  sun  be 
moving  towards  a  particular  point  on  the  celestial  sphere, 
then  by  an  obvious  effect  of  perspective  the  stars  near 
that  point  will  appear  to  recede  from  it  and  one  another 
on  the  celestial  sphere,  while  those  in  the  opposite  region 
will  approach  one  another,  the  magnitude  of  these  changes 


Motion  of  the  Sun  in  Spaa 


345 


depending  on  the  rapidity  of  the  sun's  motion  and  on 
the  nearness  of  the  stars  in  question.  The  effect  is  exactly 
of  the  same  nature  as  that  produced  when,  on  looking 
along  a  street  at  night,  two  lamps  on  opposite  sides  of  the 
street  at  some  distance  from  us  appear  close  together,  but 
as  we  walk  down  the  street  towards  them  they  appear  to 
become  more  and  more  separated  from  one  another.  In 
the  figure,  for  example,  L  and  L'  as  seen  from  B  appear 
farther  apart  than  when  seen  from  A. 


FIG.  84.— Illustrating  the  effect  of  the  sun's  motion  in  space. 

If  the  observed  proper  motions  of  stars  examined  are  not 
of  this  character,  they  cannot  be  explained  as  due  merely  to 
the  motion  of  the  sun  ;  but  if  they  shew  some  tendency 
to  move  in  this  way,  then  the  observations  can  be  most 
simply  explained  by  regarding  the  sun  as  in  motion,  and 
by  assuming  that  the  discrepancies  between  the  effects 
resulting  from  the  assumed  motion  of  the  sun  and  the 
observed  proper  motions  are  due  to  the  motions  in  space 
of  the  several  stars. 

From  the  few  proper  motions  which  Mayer  had  at  his 
command  he  was,  however,  unable  to  derive  any  indication 
of  a  motion  of  the  sun. 

Herschel  used  the  proper  motions,  published  by  Maskelyne 
and  Lalande,  of  14  stars  (13  if  the  double  star  Castor  be 
counted  as  only  one),  and  with  extraordinary  insight  detected 
in  them  a  certain  uniformity  of  motion  of  the  kind  already 
described,  such  as  would  result  from  a  motion  of  the  sun. 
The  point  on  the  celestial  sphere  towards  which  the  sun 
was  assumed  to  be  moving,  the  apex  as  he  called  it,  was 
taken  to  be  the  point  marked  by  the  star  X  in  the  constella- 


346  A  Short  History  of  Astronomy  [Cn.  xn 

lion  Hercules.  A  motion  of  the  sun  in  this  direction 
would,  he  found,  produce  in  the  14  stars  apparent  motions 
which  were  in  the  majority  of  cases  in  general  agreement 
with  those  observed.*  This  result  was  published  in  1783, 
and  a  few  months  later  Pierre  Prevost  (175 1-1839)  deduced 
a  very  similar  result  from  Tobias  Mayer's  collection  of 
proper  motions.  More  than  20  years  later  (1805)  Herschel 
took  up  the  question  again,  using  six  of  the  brightest  stars 
in  a  collection  of  the  proper  motions  of  36  published  by 
Maskelyne  in  1790,  which  were  much  more  reliable  than 
any  earlier  ones,  and  employing  more  elaborate  processes 
of  calculation ;  again  the  apex  was  placed  in  the  constellation 
Hercules,  though  at  a  distance  of  nearly  30°  from  the 
position  given  in  1783.  Herschel's  results  were  avowedly 
to  a  large  extent  speculative,  and  were  received  by  con- 
temporary astronomers  with  a  large  measure  of  distrust  ; 
out  a  number  of  far  more  elaborate  modern  investigations 
of  the  same  subject  have  confirmed  the  general  correctness 
of  his  work,  the  earlier  of  his  two  estimates  appearing, 
however,  to  be  the  more  accurate.  He  also  made  some 
Attempts  in  the  same  papers  and  in  a  third  (published  in 
1806)  to  estimate  the  speed  as  well  as  the  direction  of  the 
sun's  motion  ;  but  the  work  necessarily  involved  so  many 
assumptions  as  to  the  probable  distances  of  the  stars — 
which  were  quite  unknown— that  it  is  not  worth  while  to 
quote  results  more  definite  than  the  statement  made  in 
the  paper  of  1783,  that  "We  may  in  a  general  way  estimate 
that  the  solar  motion  can  certainly  not  be  less  than  that 
which  the  earth  has  in  her  annual  orbit." 

266.  The  question  of  the  comparative  brightness  of  stars 
was,  as  we  have  seen  (§  258),  of  importance  in  connection 
with  Herschel's  attempts  to  estimate  their  relative  distances 
from  the  earth  and  their  arrangement  in  space ;  it  also 
presented  itself  in  connection  with  inquiries  into  the  vari- 
ability of  the  light  of  stars.  Two  remarkable  cases  of 
variability  had  been  for  some  time  known.  A  star  in  the 
Whale  (o  Ceti  or  Mird]  had  been  found  to  be  at  times 

*  More  precisely,  counting  motions  in  right  ascension  and  in 
declination  separately,  he  had  27  observed  motions  to  deal  with  (one 
of  the  stars  having  no  motion  in  declination)  ;  22  agreed  in  sign  with 
those  which  would  result  from  the  assumed  motion  of  the  sun. 


$  266]  Variable  Stars  347 

invisible  to  the  naked  eye  and  at  other  times  to  be  con- 
spicuous ;  a  Dutch  astronomer,  Phocy tides  Hohvarda  (1618- 
1651),  first  clearly  recognised  its  variable  character  (1639), 
and  Ismael  Boulliau  or  Bullialdus  (1605-1694)  in  1667  fixed 
its  period  at  about  eleven  months,  though  it  was  found  that 
its  fluctuations  were  irregular  both  in  amount  and  in  period. 
Its  variations  formed  the  subject  of  the  first  paper  published 
by  Herschel  in  the  Philosophical  Transactions  (1780).  An 
equally  remarkable  variable  star  is  that  known  as  Algol 
(or  /?  Persei),  the  fluctuations  of  which  were  found  to  be 
performed  with  almost  absolute  regularity.  Its  variability 
had  been  noted  by  Geminiano  Montanari  (1632-1687)  in 
1669,  but  the  regularity  of  its  changes  was  first  detected 
in  1783  by  John  Goodricke  (1764-1786),  who  was  soon 
able  to  fix  its  period  at  very  nearly  2  days  20  hours  49 
minutes.  Algol,  when  faintest,  gives  about  one-quarter  as 
much  light  as  when  brightest,  the  change  from  the  first 
state  to  the  second  being  effected  in  about  ten  hours ; 
whereas  Mira  varies  its  light  several  hundredfold,  but 
accomplishes  its  changes  much  more  slowly. 

At  the  beginning  of  Herschel's  career  these  and  three  or 
four  others  of  less  interest  were  the  only  stars  definitely 
recognised  as  variable,  though  a  few  others  were  added  soon 
afterwards.  Several  records  also  existed  of  so-called  "  new  " 
stars,  which  had  suddenly  been  noticed  in  places  where  no 
star  had  previously  been  observed,  and  which  for  the  most 
part  rapidly  became  inconspicuous  again  (cf.  chapter  11.,  §  42  \ 
chapter  v.,  §  100  ;  chapter  vii.,  §  138);  such  stars  might 
evidently  be  regarded  as  variable  stars,  the  times  of  greatest 
brightness  occurring  quite  irregularly  or  at  long  intervals. 
Moreover  various  records  of  the  brightness  of  stars  by  earlier 
astronomers  left  little  doubt  that  a  good  many  must  have 
varied  sensibly  in  brightness.  For  example,  a  small  star  in 
the  Great  Bear  (close  to  the  middle  star  of  the  "  tail  ")  was 
among  the  Arabs  a  noted  test  of  keen  sight,  but  is  perfectly 
visible  even  in  our  duller  climate  to  persons  with  ordinary 
eyesight ;  and  Castor,  which  appeared  the  brighter  of  the 
two  Twins  to  Bayer  when  he  published  his  Atlas  (1603), 
was  in  the  i8th  century  (as  now)  less  bright  than  Pollux. 

Herschel  made  a  good  many  definite  measurements  of 
the  amounts  of  light  emitted  by  stars  of  various  magnitudes, 


348  A  Short  History  of  Astronomy  [CH.  xii 

but  was  not  able  to  carry  out  any  extensive  or  systematic 
measurements  on  this  plan.  With  a  view  to  the  future 
detection  of  such  changes  of  brightness  as  have  just  been 
mentioned,  he  devised  and  carried  out  on  a  large  scale 
the  extremely  simple  method  of  sequences.  If  a  group  of 
stars  are  observed  and  their  order  of  brightness  noted  at 
two  different  times,  then  any  alteration  in  the  order  will 
shew  that  the  brightness  of  one  or  more  has  changed.  So 
that  if  a  number  of  stars  are  observed  in  sets  in  such  a  way 
that  each  .star  is  recorded  as  being  less  bright  than  certain 
stars  near  it  and  brighter  than  certain  other  stars,  materials 
are  thereby  provided  for  detecting  at  any  future  time  any 
marked  amount  of  variation  of  brightness.  Herschel  pre- 
pared on  this  plan,  at  various  times  between  1796  and  1799, 
four  catalogues  of  comparative  brightness  based  on  naked- 
eye  observations  and  comprising  altogether  about  3,000 
stars.  In  the  course  of  the  work  a  good  many  cases  of 
slight  variability  were  noticed  ;  but  the  most  interesting 
discovery  of  this  kind  was  that  of  the  variability  of  the 
well-known  star  a  Herculis,  announced  in  1796.  The  period 
was  estimated  at  60  days,  and  the  star  thus  seemed  to  form 
a  connecting  link  between  the  known  variables  which  like 
Algol  had  periods  of  a  very  few  days  and  those  (of  which 
Mira  was  the  best  known)  with  periods  of  some  hundreds 
of  days.  As  usual,  Herschel  was  not  content  with  a  mere 
record  of  observations,  but  attempted  to  explain  the  observed 
facts  by  the  supposition  that  a  variable  star  had  a  rotation 
and  that  its  surface  was  of  unequal  brightness. 

267.  The  novelty  of  Herschel's  work  on  the  fixed  stars, 
and  the  very  general  character  of  the  results  obtained,  have 
caused  this  part  of  his  researches  to  overshadow  in  some 
respects  his  other  contributions  to  astronomy. 

Though  it  was  no  part  of  his  plan  to  contribute  to  that 
precise  knowledge  of  the  motions  of  the  bodies  of  the  solar 
system  which  absorbed  the  best  energies  of  most  of  the 
astronomers  of  the  i8th  century — whether  they  were 
observers  or  mathematicians — he  was  a  careful  and  success- 
ful observer  of  the  bodies  themselves. 

His  discoveries  of  Uranus,  of  two  of  its  satellites,  and  of 
two  new  satellites  of  Saturn  have  been  already  mentioned 
in  connection  with  his  life  (§§  253,  255).  He  believed 


*  267]      Brightness  of  Stars :  Planetary  Observations       349 

himself  to  have  seen  also  (1798)  four  other  satellites  of 
Uranus,  but  their  existence  was  never  satisfactorily  verified  ; 
and  the  second  pair  of  satellites  now  known  to  belong  to 
Uranus,  which  were  discovered  by  Lassell  in  1847  (chap- 
ter xiii.,  §  295),  do  not  agree  in  position  and  motion  with 
any  of  Herschel's  four.  It  is  therefore  highly  probable  that 
ihey  were  mere  optical  illusions  due  to  defects  of  his  mirror, 
though  it  is  not  impossible  that  he  may  have  caught  glimpses 
of  one  or  other  of  Lassell's  satellites  and  misinterpreted  the 
observations. 

Saturn  was  a  favourite  object  of  study  with  Herschel  from 
the  very  beginning  of  his  astronomical  career,  and  seven 
papers  on  the  subject  were  published  by  him  between  1790 
and  1806.  He  noticed  and  measured  the  deviation  of  the 
planet's  form  from  a  sphere  (1790);  he  observed  various 
markings  on  the  surface  of  the  planet  itself,  and  seems  to 
have  seen  the  inner  ring,  now  known  from  its  appearance 
as  the  crape  ring  (chapter  XIIL,  §  295),  though  he  did  not 
recognise  its  nature.  By  observations  of  some  markings  at 
some  distance  from  the  equator  he  discovered  (1790)  that 
Saturn  rotated  on  an  axis,  and  fixed  the  period  of  rotation 
at  about  loh.  i6m.  (a  period  differing  only  by  about  2 
minutes  from  modern  estimates),  and  by  similar  observations 
of  the  ring  (1790)  concluded  that  it  rotated  in  about  io| 
hours,  the  axis  of  rotation  being  in  each  case  perpendicular 
to  the  plane  of  the  ring.  The  satellite  Japetus,  discovered 
by  Cassini  in  1671  (chapter  VIIL,  §  160),  had  long  been 
recognised  as  variable  in  brightness,  the  light  emitted  being 
several  times  as  much  at  one  time  as  at  another.  Herschel 
found  that  these  variations  were  not  only  perfectly  regular, 
but  recurred  at  an  interval  equal  to  that  of  the  satellite's 
period  of  rotation  round  its  primary  (1792),  a  conclusion 
which  Cassini  had  thought  of  but  rejected  as  inconsistent 
with  his  observations.  This  peculiarity  was  obviously  capable 
of  being  explained  by  supposing  that  different  portions  of 
Japetus  had  unequal  power  of  reflecting  light,  and  that  like  our 
moon  't  turned  on  its  axis  once  in  every  revolution,  in  such 
a  way  as  always  to  present  the  same  face  towards  its 
primary,  and  in  consequence  each  face  in  turn  to  an 
observer  on  the  earth.  It  was  natural  to  conjecture  that 
such  an  arrangement  was  general  among  satellites,  and 


350  A  Short  History  of  Astronomy  CH.  xn. 

Herschel  obtained  (1797)  some  evidence  of  variability  in 
the  satellites  of  Jupiter,  which  appeared  to  him  to  support 
this  hypothesis. 

Herschel's  observations  of  other  planets  were  less 
numerous  and  important.  He  rightly  rejected  the  supposed 
observations  by  Schroeter  (§271)  of  vast  mountains  on 
Venus,  and  was  only  able  to  detect  some  indistinct  markings 
from  which  the  planet's  rotation  on  an  axis  could  be 
somewhat  doubtfully  inferred.  He  frequently  observed  the 
familiar  bright  bands  on  Jupiter  commonly  called  belts, 
which  he  was  the  first  to  interpret  (1793)  as  bands  of 
cloud.  On  Mars  he  noted  the  periodic  diminution  of  the 
white  caps  on  the  two  poles,  and  observed  how  in  these 
and  other  respects  Mars  was  of  all  planets  the  one  most 
like  the  earth. 

268.  Herschel  made  also  a  number  of  careful  observa- 
tions on  the  sun,  and  based  on  them  a  famous  theory  of  its 
structure.  He  confirmed  the  existence  of  various  features 
of  the  solar  surface  which  had  been  noted  by  the  earlier 
telescopists  such  as  Galilei,  Scheiner,  and  Hevel,  and 
added  to  them  in  some  points  of  detail.  Since  Galilei's 
time  a  good  many  suggestions  as  to  the  nature  of  spots  had 
been  thrown  out  by  various  observers,  such  as  that  they 
were  clouds,  mountain-tops,  volcanic  products,  etc.,  but 
none  of  these  had  been  supported  by  any  serious  evidence. 
Herschel's  observations  of  the  appearances  of  spots  suggested 
to  him  that  they  were  depressions  in  the  surface  of  the  sun, 
a  view  which  derived  support  from  occasional  observations 
of  a  spot  when  passing  over  the  edge  of  the  sun  as  a 
distinct  depression  or  notch  there.  Upon  this  somewhat 
slender  basis  of  fact  he  constructed  (1795)  an  elaborate 
theory  of  the  nature  of  the  sun,  which  attracted  very  general 
notice  by  its  ingenuity  and  picturesqueness  and  commanded 
general  assent  in  the  astronomical  world  for  more  than  half 
a  century.  The  interior  of  the  sun  was  supposed  to  be  a 
cold  dark  solid  body,  surrounded  by  two  cloud-layers,  of 
which  the  outer  was  the  photosphere  or  ordinary  surface  of 
the  sun,  intensely  hot  and  luminous,  and  the  inner  served  as 
a  fire-screen  to  protect  the  interior.  The  umbra  (chapter  vi., 
§  124)  of  a  spot  was  the  dark  interior  seen  through  an 
opening  in  the  clouds,  and  the  penumbra  corresponded 


§*  263,  269]  Herschel's  Theory  of  the  Sun  35 1 

to  the  inner  cloud-layer  rendered  luminous  by  light  from 
above. 

"  The  sun  viewed  in  this  light  appears  to  be  nothing  else 
than  a  very  eminent,  large,  and  lucid  planet,  evidently  the  first 
<  r,  in  strictness  of  speaking,  the  only  primary  one  of  our 
?"stem  ;  ...  it  is  most  probably  also  inhabited,  like  the  rest 
"t"  the  planets,  by  beings  whose  organs  are  adapted  to  the 
peculiar  circumstances  of  that  vast  globe." 

That  spots  were  depressions  had  been  suggested  more 
than  twenty  years  before  (1774)  by  Alexander  Wilson  of 
Glasgow  (1714-1786),  and  supported  by  evidence  different 
from  any  adduced  by  Herschel  and  in  some  ways  more 
conclusive.  Wilson  noticed,  first  in  the  case  of  a  large 
spot  seen  in  1769,  and  afterwards  in  other  cases,  that  as 
the  sun's  rotation  carries  a  spot  across  its  disc  from  one 
edge  to  another,  its  appearance  changes  exactly  as  it  would 
do  in  accordance  with  ordinary  laws  of  perspective  if  the 
spot  were  a  saucer-shaped  depression,  of  which  the  bottom 
formed  the  umbra  and  the  sloping  sides  the  penumbra, 
since  the  penumbra  appears  narrowest  on  the  side  nearest 
the  centre  of  the  sun  and  widest  on  the  side  nearest  the 
edge.  Hence  Wilson  inferred,  like  Herschel,  but  with 
less  confidence,  that  the  body  of  the  sun  is  dark.  In 
the  paper  referred  to  Herschel  shews  no  signs  of  being 
acquainted  with  Wilson's  work,  but  in  a  second  paper 
(1801),  which  contained  also  a  valuable  series  of  observa- 
tions of  the  detailed  markings  on  the  solar  surface,  he 
refers  to  Wilson's  "geometrical  proof"  of  the  depression 
of  the  umbra  of  a  spot. 

Although  it  is  easy  to  see  now  that  Herschel's  theory  was 
a  rash  generalisation  from  slight  data,  it  nevertheless  ex- 
plained— with  fair  success — most  of  the  observations  made 
up  to  that  time. 

Modern  knowledge  of  heat,  which  was  not  accessible 
to  Herschel,  shews  us  the  fundamental  impossibility  of 
the  continued  existence  of  a  body  with  a  cold  interior  and 
merely  a  shallow  ring  of  hot  and  luminous  material  round 
it ;  and  the  theory  in  this  form  is  therefore  purely  of 
historic  interest  (cf.  also  chapter  xiii.,  §§  298,  303). 

269.  Another  suggestive  idea  of  Herschel's  was  the 
analogy  between  the  sun  and  a  variable  star,  the  known 


352  A  Short  History  of  Astronomy  [Cn.  xn. 

variation  in  the  number  of  spots  and  possibly  of  other 
markings  on  the  sun  suggesting  to  him  the  probability 
of  a  certain  variability  in  the  total  amount  of  solar  light 
and  heat  emitted.  The  terrestrial  influence  of  this  he 
tried  to  measure — in  the  absence  of  precise  meteoro- 
logical data — with  characteristic  ingenuity  by  the  price  of 
wheat,  and  some  evidence  was  adduced  to  shew  that  at 
times  when  sun-spots  had  been  noted  to  be  scarce — 
corresponding  according  to  Herschel's  view  to  periods 
of  diminished  solar  activity — wheat  had  been  dear  and 
the  weather  presumably  colder.  In  reality,  however, 
the  data  were  insufficient  to  establish  any  definite  con- 
clusions. 

270.  In   addition  to   carrying   out  the  astronomical  re- 
searches already  sketched,  and  a  few  others  of  less  import- 
ance, Herschel  spent  some  time,  chiefly  towards  the  end  of 
his  life,  in  working  at  light  and  heat ;  but  the  results  obtained, 
though  of  considerable  value,  belong  rather  to  physics  than 
to  astronomy,  and  need  not  be  dealt  with  here. 

271.  It  is  natural  to  associate  Herschel's  wonderful  series 
of  discoveries  with  his  possession  of  telescopes  of  unusual 
power  and  with  his  formulation  of  a  new  programme  of 
astronomical    inquiry ;  and   these    were    certainly   essential 
elements.     It  is,  however,  significant,  as  shewing  how  im- 
portant   other   considerations   were,    that   though   a   great 
number   of  his   telescopes  were   supplied  to   other   astro- 
nomers,   and   though   his   astronomical    programme   when 
once  suggested  was  open  to  all  the  world  to  adopt,  hardly 
any    of    his    contemporaries    executed    any    considerable 
amount  of  work  comparable  in  scope  to  his  own. 

Almost  the  only  astronomer  of  the  period  whose  work 
deserves  mention  beside  Herschel's,  though  very  inferior  to 
it  both  in  extent  and  in  originality,  \tzs  Johann  Hieronymus 
Schroeter  (1745-1816). 

Holding  an  official  position  at  Lilienthal,  near  Bremen, 
he  devoted  his  leisure  during  some  thirty  years  to  a  scrutiny 
of  the  planets  and  of  the  moon,  and  to  a  lesser  extent  of 
other  bodies. 

As  has  been  seen  in  the  case  of  Venus  (§  267),  his  results 
were  not  always  reliable,  but  notwithstanding  some  errors 
he  added  considerably  to  our  knowledge  of  the  appearances 


§*  wo,  271]  Hcrschel  and  Schroeter  353 

presented  by  the  various  planets,  and  in  particular  studied 
the  visible  features  of  the  moon  with  a  minuteness  and 
accuracy  far  exceeding  that  of  any  of  his  predecessors,  and 
made  some  attempt  to  deduce  from  his  observations  data 
as  to  its  physical  condition.  His  two  volumes  on  the 
moon  {Selenotopographische  Fragmente,  1791  and  1802),  and 
other  minor  writings,  are  a  storehouse  of  valuable  detail, 
to  which  later  workers  have  been  largely  indebted. 


CHAPTER   XIII. 

THE   NINETEENTH    CENTURY. 

"The  greater  the  sphere  ot  our  knowledge,  the  larger  is  the 
surface  of  its  contact  with  the  infinity  of  our  ignorance." 

272.  THE  last  three  chapters  have  contained  some  account 
of  progress  made  in  three  branches  of  astronomy  which, 
though  they  overlap  and  exercise  an  important  influence  on 
one  another,  are  to  a  large  extent  studied  by  different  men 
and  by  different  methods,  and  have  different  aims.  The 
difference  is  perhaps  best  realised  by  thinking  of  the  work 
of  a  great  master  in  each  department,  Bradley,  Laplace, 
and  Herschel.  So  great  is  the  difference  that  Delambre 
in  his  standard  history  of  astronomy  all  but  ignores  the 
work  of  the  great  school  of  mathematical  astronomers  who 
were  his  contemporaries  and  immediate  predecessors,  not 
from  any  want  of  appreciation  of  their  importance,  but 
because  he  regards  their  work  as  belonging  rather  to  mathe- 
matics than  to  astronomy;  while  Bessel  (§  277),  in  saying 
that  the  function  of  astronomy  is  "  to  assign  the  places  on 
the  sky  where  sun,  moon,  planets,  comets,  and  stars  have 
been,  are,  and  will  be,"  excludes  from  its  scope  nearly 
everything  towards  which  Herschel's  energies  were  directed. 

Current  modern  practice  is,  however,  more  liberal  in  its 
use  of  language  than  either  Delambre  or  Bessel,  and  finds  it 
convenient  to  recognise  all  three  of  the  subjects  or  groups 
of  subjects  referred  to  as  integral  parts  of  one  science. 

The  mutual  relation  of  gravitational  astronomy  and  what 
has  been  for  convenience  called  observational  astronomy 
has  been  already  referred  to  (chapter  x.,  §  196).  It  should, 
however,  be  noticed  that  the  latter  term  has  in  this  book 
hitherto  been  used  chiefly  for  only  one  part  of  the  astrono- 

354 


CH.  xiii.,  $$  272, 273]     Descriptive  Astronomy  355 

mical  work  which  concerns  itself  primarily  with  observation. 
Observing  played  at  least  as  large  a  part  in  HerschePs 
work  as  in  Bradley's,  but  the  aims  of  the  two  men  were 
in  many  ways  different.  Bradley  was  interested  chiefly  in 
ascertaining  as  accurately  as  possible  the  apparent  positions 
of  the  fixed  stars  on  the  celestial  sphere,  and  the  positions 
and  motions  of  the  bodies  of  the  solar  system,  the  former 
undertaking  being  in  great  part  subsidiary  to  the  latter. 
Herschel,  on  the  other  hand,  though  certain  of  his  re- 
searches, e.g.  into  the  parallax  of  the  fixed  stars  and  into 
the  motions  of  the  satellites  of  Uranus,  were  precisely  like 
some  of  Bradley's,  was  far  more  concerned  with  questions 
of  the  appearances,  mutual  relations,  and  structure  of  the 
celestial  bodies  in  themselves.  This  latter  branch  of 
astronomy  may  conveniently  be  called  descriptive  astronomy, 
though  the  name  is  not  altogether  appropriate  to  inquiries 
into  the  physical  structure  and  chemical  constitution  of 
celestial  bodies  which  are  often  put  under  this  head,  and 
which  play  an  important  part  in  the  astronomy  of  the 
present  day. 

273.  Gravitational  astronomy  and  exact  observational 
astronomy  have  made  steady  progress  during  the  nineteenth 
century,  but  neither  has  been  revolutionised,  and  the 
advances  made  have  been  to  a  great  extent  of  such  a 
nature  as  to  be  barely  intelligible,  still  less  interesting,  to 
those  who  are  not  experts  The  account  of  them  to  be 
given  in  this  chapter  must  therefore  necessarily  be  of  the 
slightest  character,  and  deal  either  with  general  tendencies  or 
with  isolated  results  of  a  less  technical  character  than  the  rest. 

Descriptive  astronomy,  on  the  other  hand,  which  can  be 
regarded  as  being  almost  as  much  the  creation  of  Herschel 
as  gravitational  astronomy  is  of  Newton,  has  not  only  been 
greatly  developed  on  the  lines  laid  down  by  its  founder,  but 
has  received — chiefly  through  the  invention  of  spectrum 
analysis  (§  299) — extensions  into  regions  not  only  unthought 
of  but  barely  imaginable  a  century  ago.  Most  of  the 
results  of  descriptive  astronomy — unlike  those  of  the  older 
branches  of  the  subject — are  readily  intelligible  and  fairly 
interesting  to  those  who  have  but  little  knowledge  of  the 
subject;  in  particular  they  are  as  yet  to  a  considerable 
extent  independent  of  the  mathematical  ideas  and  language 


356  A  Short  History  of  Astronomy          [CH.  xin. 

which  dominate  so  much  of  astronomy  "and  render  it 
unattractive  or  inaccessible  to  many.  Moreover,  not  only 
can  descriptive  astronomy  be  appreciated  and  studied,  but 
its  progress  can  materially  be  assisted,  by  observers  who 
have  neither  knowledge  of  higher  mathematics  nor  any 
elaborate  instrumental  equipment. 

Accordingly,  while  the  successors  of  Laplace  and  Bradley 
have  been  for  the  most  part  astronomers  by  profession, 
attached  to  public  observatories  or  to  universities,  an 
immense  mass  of  valuable  descriptive  work  has  been  done 
by  amateurs  who,  like  Herschel  in  the  earlier  part  of  his 
career,  have  had  to  devote  a  large  part  of  their  energies  to 
professional  work  of  other  kinds,  and  who,  though  in  some 
cases  provided  with  the  best  of  instruments,  have  in  many 
others  been  furnished  with  only  a  slender  instrumental 
outfit.  For  these  and  other  reasons  one  of  the  most 
notable  features  of  nineteenth  century  astronomy  has  been 
a  great  development,  particularly  in  this  country  and  in  the 
United  States,  of  general  interest  in  the  subject,  and  the 
establishment  of  a  large  number  of  private  observatories 
devoted  almost  entirely  to  the  study  of  special  branches  of 
descriptive  astronomy.  The  nineteenth  century  has  ac- 
cordingly witnessed  the  acquisition  of  an  unprecedented 
amount  of  detailed  astronomical  knowledge.  But  the 
wealth  of  material  thus  accumulated  has  outrun  our  powers 
of  interpretation,  and  in  a  number  of  cases  our  knowledge 
of  some  particular  department  of  descriptive  astronomy 
consists,  on  the  one  hand  of  an  immense  series  of  careful 
observations,  and  on  the  other  of  one  or  more  highly 
speculative  theories,  seldom  capable  of  explaining  more 
than  a  small  portion  of  the  observed  facts. 

In  dealing  with  the  progress  of  modern  descriptive 
astronomy  the  proverbial  difficulty  of  seeing  the  wood  on 
account  of  the  trees  is  therefore  unusually  great.  To  give 
an  account  within  the  limits  of  a  single  chapter  of  even  the 
most  important  facts  added  to  our  knowledge  would  be  a 
hopeless  endeavour ;  fortunately  it  would  also  be  superfluous, 
as  they  are  to  be  found  in  many  easily  accessible  textbooks 
on  astronomy,  or  in  treatises  on  special  parts  of  the  subject. 
All  that  can  be  attempted  is  to  give  some  account  of  the 
chief  lines  on  which  progress  has  been  made,  and  to 


$$  274,  275]    Descriptive  Astronomy:  Theory  of  Errors      357 

indicate   some    general    conclusions    which    seem    to    be 
established  on  a  tolerably  secure  basis. 

274.  The  progress   of  exact   observation  has  of  course 
been  based  very  largely  on  instrumental  advances.      Not 
only  have  great  improvements  been  made  in  the  extremely 
delicate  work  of  making  large   lenses,  but   the  graduated 
circles   and   other   parts   of  the   mounting  of  a   telescope 
upon  which  accuracy  of  measurement  depends  can  also  be 
constructed  with  far  greater  exactitude  and  certainty  than 
at  the  beginning  of  the  century.    New  methods  of  mounting 
telescopes  and  of  making  and  recording  observations  have 
also  been  introduced,  all  contributing  to  greater  accuracy.  , 
For   certain    special    problems    photography   is    found   to 
present  great  advantages  as  compared  with  eye- observations, 
though  its  most  important  applications  have  so  far  been  to 
descriptive  astronomy. 

275.  The   necessity   for   making    allowance   for    various 
known  sources  of  errors  in  observation,  and  for  diminishing 
as  far  as  possible  the  effect  of  errors  due  to  unknown  causes, 
had   been   recognised  even   by   Tycho  Brahe  (chapter  v., 
§  no),   and  had   played   an  important   part   in   the   work 
of    Flamsteed    and    Bradley   (chapter    x.,   §§    198,    218). 
Some  further  important  steps  in  this  direction  were  taken 
in    the    earlier    part   of    this    century.      The    method   of 
least    squares,     established   independently    by   two    great 
mathematicians,   Adrien   Marie  Legendre   (1752-1833)    of 
Paris  and  Carl  Friedrich  Gauss  (1777-1855)  of  Gottingen,* 
was    a    systematic    method    of    combining    observations, 
which    gave    slightly    different     results,    in    such    a    way 
as    to   be  as  near   the   truth   as   possible.      Any   ordinary 
physical  measurement,  e.g.  of  a  length,  however   carefully 
executed,  is  necessarily  imperfect ;  if  the  same  measurement 
is  made  several-  times,  even  under  almost  identical  condi- 
tions, the  results  will  in  general  differ  slightly ;   and  the 
question  arises  of  combining  these  so  as  to  get  the  most 
satisfactory  result.     The  common  practice  in  this  simple 
case  has  long  been  to  take  the  arithmetical  mean  or  average 
of  the  different  results.     But  astronomers  have  constantly 

*  The  method  was  published  by  Legendre  in  1806  and  by  Gauss 
in  1809,  but  it  was  invented  and  used  by  the  latter  more  than  20 
years  earlier. 


35 8  A  Short  History  of  Astronomy  [Cn.  xin. 

to  deal  with  more  complicated  cases  in  which  two  or  more 
unknown  quantities  have  to  be  determined  from  observa- 
tions of  different  quantities,  as,  for  example,  when  the 
elements  of  the  orbit  of  a  planet  (chapter  XL,  §  236)  have 
to  be  found  from  observations  of  the  planet's  position  at 
different  times.  The  method  of  least  squares  gives  a  rule 
for  dealing  with  such  cases,  which  was  a  generalisation 
of  the  ordinary  rule  of  averages  for  the  case  of  a  single 
unknown  quantity  ;  and  it  was  elaborated  in  such  a  way 
as  to  provide  for  combining  observations  of  different  value, 
such  as  observations  taken  by  observers  of  unequal  skill 
or  with  different  instruments,  or  under  more  or  less  favour- 
able conditions  as  to  weather,  etc.  It  also  gives  a  simple 
means  of  testing,  by  means  of  their  mutual  consistency, 
the  value  of  a  series  of  observations,  and  comparing  their 
probable  accuracy  with  that  of  some  other  series  executed 
under  different  conditions.  The  method  of  least  squares 
and  the  special  case  of  the  "  average "  can  be  deduced 
from  a  certain  assumption  as  to  the  general  character  of 
the  causes  which  produce  the  error  in  question ;  but  the 
assumption  itself  cannot  be  justified  a  priori;' on  the  other 
hand,  the  satisfactory  results  obtained  from  the  application 
of  the  rule  to  a  great  variety  of  problems  in  astronomy 
and  in  physics  has  shewn  that  in  a  large  number  of  cases 
unknown  causes  of  error  must  be  approximately  of  the 
type  considered.  The  method  is  therefore  very  widely 
used  in  astronomy  and  physics  wherever  it  is  worth 
while  to  take  trouble  to  secure  the  utmost  attainable 
accuracy. 

276.  Legendre's  other  contributions  to  science  were 
almost  entirely  to  branches  of  mathematics  scarcely  affect- 
ing astronomy.  Gauss,  on  the  other  hand,  was  for  nearly 
half  a  century  head  of  the  observatory  of  Gottingen,  and 
though  his  most  brilliant  and  important  work  was  in  pure 
mathematics,  while  he  carried  out  some  researches  of  first- 
rate  importance  in  magnetism  and  other  branches  of  physics, 
he  also  made  some  further  contributions  of  importance  to 
astronomy.  These  were  for  the  most  part  processes  of 
calculation  of  various  kinds  required  for  utilising  astrono- 
mical observations,  the  best  known  being  a  method  of 
calculating  the  orbit  of  a  planet  from  three  complete 


§§  276, 277  Legendre  and  Gauss  359 

observations  of  its  position,  which  was  published  in  his 
Theoria  Motus  (1809).  As  we  have  seen  (chapter  XL, 
§  236),  the  complete  determination  of  a  planet's  orbit 
depends  on  six  independent  elements  :  any  complete  ob- 
servation of  the  planet's  position  in  the  sky,  at  any  time, 
gives  two  quantities,  e.g.  the  right  ascension  and  declination 
(chapter  11.,  §  33) ;  hence  three  complete  observations 
give  six  equations  and  are  theoretically  adequate  to  de- 
termine the  elements  of  the  orbit ;  but  it  had  not  hitherto 
been  found  necessary  to  deal  with  the  problem  in  this 
form.  The  orbits  of  all  the  planets  but  Uranus  had  been 
worked  out  gradually  by  the  use  of  a  series  of  observations 
extending  over  centuries ;  and  it  was  feasible  to  use  ob- 
servations taken  at  particular  times  so  chosen  that  certain 
elements  could  be  determined  without  any  accurate  know- 
ledge of  the  others ;  even  Uranus  had  been  under  observa- 
tion for  a  considerable  time  before  its  path  was  determined 
with  anything  like  accuracy ;  and  in  the  case  of  comets 
not  only  was  a  considerable  series  of  observations  generally 
available,  but  the  problem  was  simplified  by  the  fact  that 
the  orbit  could  be  taken  to  be  nearly  or  quite  a  parabola 
instead  of  an  ellipse  (chapter  ix.,  §  190).  The  discovery 
of  the  new  planet  Ceres  on  January  ist,  1801  (§  294),  and 
its  loss  when  it  had  only  been  observed  for  a  few  weeks, 
presented  virtually  a  new  problem  in  the  calculation  of  an 
orbit.  Gauss  applied  his  new  methods — including  that 
of  least  squares — to  the  observations  available,  and  with 
complete  success,  the  planet  being  rediscovered  at  the 
end  of  the  year  nearly  in  the  position  indicated  by  his 
calculations. 

277.  The  theory  of  the  "reduction"  of  observations 
(chapter  x.,  §  218)  was  first  systematised  and  very  much 
improved  by  Friedrich  Wilhelm  Bessel  (1784-1846),  who 
was  for  more  than  thirty  years  the  director  of  the  new 
Prussian  observatory  at  Konigsberg.  His  first  great  work 
was  the  reduction  and  publication  of  Bradley's  Greenwich 
observations  (chapter  x.,  §  218).  This  undertaking  involved 
an  elaborate  study  of  such  disturbing  causes  as  precession, 
aberration,  and  refraction,  as  well  as  of  the  errors  of  Bradley's 
instruments.  Allowance  was  made  for  these  on  a  uniform  and 
systematic  plan,  and  the  result  was  the  publication  in  1818, 


360  A  Short  History  of  Astronomy          [CH.  xi.i. 

under  the  title  Fundamcnta  Astronomiae,  of  a  catalogue  of 
the  places  of  3,222  stars  as  they  were  in  1755.  A  special 
problem  dealt  with  in  the  course  of  the  work  was  that  of 
refraction.  Although  the  complete  theoretical  solution 
was  then  as  now  unattainable,  Bessel  succeeded  in  con- 
structing a  table  of  refractions  which  agreed  very  closely 
with  observation  and  was  presented  in  such  a  form  that 
the  necessary  correction  for  a  star  in  almost  any  position 
could  be  obtained  with  very  little  trouble.  His  general 
methods  of  reduction — published  finally  in  his  Tabulae 
Regiomontanae  (1830) — also  had  the  great  advantage  of 
arranging  the  necessary  calculations  in  such  a  way  that 
they  could  be  performed  with  very  little  labour  and  by  an 
almost  mechanical  process,  such  as  could  easily  be  carried 
out  by  a  moderately  skilled  assistant.  In  addition  to 
editing  Bradley's  observations,  Bessel  undertook  a  fresh 
series  of  observations  of  his  own,  executed  between  the 
years  1821  and  1833,  upon  which  were  based  two  new 
catalogues,  containing  about  62,000  stars,  which  appeared 
after  his  death. 

278.  The  most  memorable  of  Bessel's  special  pieces  of 


a: 
FIG.  85. — 61  Cygni  and  the  two  neighbouring  stars  used  by  Bessel. 

work  was  the  first  definite  detection  of  the  parallax  of  a 
fixed    star.     He  abandoned    the    test  of  brightness  as  an 


The  Parallax  of  61    Cygni 


361 


indication  of  nearness,  and  selected  a  star  (61  Cygni) 
which  was  barely  visible  to  the  naked  eye  but  was  re- 
markable for  its  large  proper  motion  (about  5"  per  annum) ; 
evidently  if  a  star  is  moving  at  an  assigned  rate  (in  miles 
per  hour)  through  space,  the  nearer  to  the  observer  it  is  the 
more  rapid  does  its  motion  appear  to  be,  so  that  apparent 
rapidity  of  motion,  like  brightness,  is  a 
probable  but  by  no  means  infallible 
indication  of  nearness.  A  modification 
of  Galilei's  differential  method  (chap- 
ter vi.,  §  129,  and  chapter  XH.,  §  263) 
being  adopted,  the  angular  distance 
of  6 1  Cygni  from  two  neighbouring 
stars,  the  faintness  and  immovability 
of  which  suggested  their  great  distance 
in  space,  was  measured  at  frequent 
intervals  during  a  year.  From  the 
changes  in  these  distances  cr  a,  a-  b 
(in  fig.  85),  the  size  of  the  small  ellipse 
described  by  o-  could  be  calculated. 
The  result,  announced  at  the  end  of 
1838,  was  that  the  star  had  an  annual 
parallax  of  about  3"  (chapter  VIIL, 
§  161),  i.e.  that  the  star  was  at  such 
distance  that  the  greatest  angular  dis- 
tance of  the  earth  from  the  sun  viewed 
from  the  star  (the  angle  s  a-  E  in  fig.  86, 
where  s  is  the  sun  and  E  the  earth) 
was  this  insignificant  angle.*  The 
result  was  confirmed,  with  slight  altera- 
tions, by  a  fresh  investigation  of 
Bessel's  in  1839-40,  but  later  work 
seems  to  shew  that  the  parallax  is  a 
little  less  than  £".t  With  this  latter 
estimate,  the  apparent  size  of  the  earth's  path  round  the 
sun  as  seen  from  the  star  is  the  same  as  that  of  a  halfpenny 

*  The  figure  has  to  be  enormously  exaggerated,  the  angle  s  <r  E  as 
shewn  there  being  about  10°,  and  therefore  about  100,000  times  too 
great. 

f  Sir  R.  S.  Ball  and  the  late  Professor  Pritchard  (§  279)  have 
obtained  respectively  -47"  and  -43"  ;  the  mean  of  these,  -45",  may  be 
provisionally  accepted  as  not  very  far  from  the  truth. 


FIG.  86.— The  parallax 
of  6 1  Cygni. 


362  A  Short  History  of  Astronomy          [CH.  xil 

at  a  distance  of  rather  more  than  three  miles.  In  other 
words,  the  distance  of  the  star  is  about  400,000  times  the 
distance  of  the  sun,  which  is  itself  about  93,000,000  miles. 
A  mile  is  evidently  a  very  small  unit  by  which  to  measure 
such  a  vast  distance ;  and  the  practice  of  expressing  such 
distances  by  means  of  the  time  required  by  light  to  perform 
the  journey  is  often  convenient.  Travelling  at  the  rate  of 
186,000  miles  per  second  (§  283),  light  takes  rather  more 
than  six  years  to  reach  us  from  61  Cygni. 

279.  Bessel's  solution  of  the  great  problem  which   had 
baffled  astronomers  ever  since  the  time  of  Coppernicus  was 
immediately  followed  by  two  others.    Early  in  1839  Thomas 
Henderson  (1798-1844)  announced  a  parallax  of  nearly  i" 
for  the  bright  star  a  Centauri  which  he  had  observed  at  the 
Cape,  and  in  the  following  year  Friedrich  Georg   Wilhelm 
Struve   (1793-1864)   obtained   from  observations  made  at 
Pulkowa  a  parallax  of  |"  for  Vega  ;  later  work  has  reduced 
these  numbers  to  'f "  and  TV  respectively. 

A  number  of  other  parallax  determinations  have  subse- 
quently been  made.  An  interesting  variation  in  method  was 
made  by  the  late  Professor  Charles  Pritchard  (1808-1893) 
of  Oxford  by  photographing  the  star  to  be  examined  and  its 
companions,  and  subsequently  measuring  the  distances  on 
the  photograph,  instead  of  measuring  the  angular  distances 
directly  with  a  micrometer. 

At  the  present  time  some  50  stars  have  been  ascertained 
with  some  reasonable  degree  of  probability  to  have  measur- 
able, if  rather  uncertain,  parallaxes ;  a  Centauri  still  holds 
its  own  as  the  nearest  star,  the  light-journey  from  it  being 
about  four  years.  A  considerable  number  of  other  stars 
have  been  examined  with  negative  or  highly  uncertain 
results,  indicating  that  their  parallaxes  are  too  small  to  be 
measured  with  our  present  means,  and  that  their  distances 
are  correspondingly  great. 

280.  A  number  of  star  catalogues  and  star   maps — too 
numerous  to   mention  separately — have  been    constructed 
during  this  century,  marking  steady  progress  in  our  know- 
ledge  of  the   position   of  the   stars,   and   providing   fresh 
materials  for   ascertaining,  by  comparison    of  the  state  of 
the  sky  at  different  epochs,  such  quantities  as  the  proper 
motions  of  the  stars  and  the  amount  of  precession.    Among 


$$  279—281]  Parallax :  Star  Catalogues  363 

the  most  important  is  the  great  catalogue  of  324,198  stars 
in  the  northern  hemisphere  known  as  the  Bonn  Durch- 
musterung,  published  in  1859-62  by  Bessel's  pupil  Friedrich 
Wilhelm  August  Argelander  ( 1 799-1875) ;  this  was  extended 
(1875-85)  so  as  to  include  133,659  stars  in  a  portion  of 
the  southern  hemisphere  by  Eduard  Schonfeld  (1828-1891) ; 
and  more  recently  Dr.  Gill  has  executed  at  the  Cape 
photographic  observations  of  the  remainder  of  the  southern 
hemisphere,  the  reduction  to  the  form  of  a  catalogue  (the 
first  instalment  of  which  was  published  in  1896)  having 
been  performed  by  Professor  Kapteyn  of  Groningen.  The 
star  places  determined  in  these  catalogues  do  not  profess 
to  be  the  most  accurate  attainable,  and  for  many  purposes 
it  is  important  to  know  with  the  utmost  accuracy  the 
positions  of  a  smaller  number  of  stars.  The  greatest 
undertaking  of  this  kind,  set  on  foot  by  the  German 
Astronomical  Society  in  1867,  aims  at  the  construction,  by 
the  co-operation  of  a  number  of  observatories,  of  catalogues 
of  about  130,000  of  the  stars  contained  in  the  "  approximate  " 
catalogues  of  Argelander  and  Schonfeld  ;  nearly  half  of  the 
work  has  now  been  published. 

The  greatest  scheme  for  a  survey  of  the  sky  yet  attempted 
is  the  photographic  chart,  together  with  a  less  extensive 
catalogue  to  be  based  on  it,  the  construction  of  which  was 
decided  on  at  an  international  congress  held  at  Paris 
in  1887.  The  whole  sky  has  been  divided  between  18 
observatories  in  all  parts  of  the  world,  from  Helsingfors  in 
the  north  to  Melbourne  in  the  south,  and  each  of  these  is 
now  taking  photographs  with  virtually  identical  instruments. 
It  is  estimated  that  the  complete  chart,  which  is  intended 
to  include  stars  of  the  i4th  magnitude,*  will  contain  about 
20,000,000  stars,  2,000,000  of  which  will  be  catalogued 
also. 

281.  One  other  great  problem — that  of  the  distance  of 
the  sun — may  conveniently  be  discussed  under  the  head 
of  observational  astronomy. 

The  transits  of  Venus  (chapter  x.,  §§  202,  227)  which 
occurred  in  1874  and  1882  were  both  extensively  observed, 

*  An  average  star  of  the  I4th  magnitude  is  10,000  times  fainter 
than  one  of  the  4th  magnitude,  \\hich  again  is  about  150  times  less 
bright  than  Sirius.  See  §  316. 


364  A  Short  History  of  Astronomy  [CH.  xm. 

the  old  methods  of  time-observation  being  supplemented 
by  photography  and  by  direct  micrometric  measurements 
of  the  positions  of  Venus  while  transiting. 

The  method  of  finding  the  distance  of  the  sun  by  means 
of  observation  of  Mars  in  opposition  (chapter  vin.,  §  161) 
has  been  employed  on  several  occasions  with  considerable 
success,  notably  by  Dr.  Gill  at  Ascension  in  1877.  A 
method  originally  used  by  Flamsteed,  but  revived  in  1857 
by  Sir  George  Biddell  Airy  (1801-1892),  the  late  Astronomer 
Royal,  was  adopted  on  'this  occasion.  For  the  determination 
of  the  parallax  of  a  planet  observations  have  to  be  made  from 
two  different  positions  at  a  known  distance  apart;  commonly 
these  are  taken  to  be  at  two  different  observatories,  as 
far  as  possible  removed  from  one  another  in  latitude. 
Airy  pointed  out  that  the  same  object  could  be  attained  if 
only  one  observatory  were  used,  but  observations  taken  at 
an  interval  of  some  hours,  as  the  rotation  of  the  earth  on 
its  axis  would  in  that  time  produce  a  known  displacement 
of  the  observer's  position  and  so  provide  the  necessary 
base  line.  The  apparent  shift  of  the  planet's  position 
could  be  most  easily  ascertained  by  measuring  (with  the 
micrometer)  its  distances  from  neighbouring  fixed  stars. 
This  method  (known  as  the  diurnal  method)  has  the  great 
advantage,  among  others,  of  being  simple  in  application,  a 
single  observer  and  instrument  being  all  that  is  needed. 

The  diurnal  method  has  also  been  applied  with  great 
success  to  certain  of  the  minor  planets  (§  294).  Revolving 
as  they  do  between  Mars  and  Jupiter,  they  are  all  farther 
off  from  us  than  the  former;  but  there  is  the"  compensating 
advantage  that  as  a  minor  planet,  unlike  Mars,  is,  as  a 
rule,  too  small  to  shew  any  appreciable  disc,  its  angular 
distance  from  a  neighbouring  star  is  more  easily  measured. 
The  employment  of  the  minor  planets  in  this  way  was  first 
suggested  by  Professor  Galle  of  Berlin  in  1872,  and  recent 
observations  of  the  minor  planets  Victoria,  Sappho,  and  Iris 
in  1888-89,  made  at  a  number  of  observatories  under  the 
general  direction  of  Dr.  Gill,  have  led  to  some  of  the  most 
satisfactory  determinations  of  the  sun's  distance. 

282.  It  was  known  to  the  mathematical  astronomers  of 
the  1 8th  century  that  the  distance  of  the  sun  could  be 
obtained  from  a  knowledge  of  various  perturbations  of 


$$  282,  283]  The  Distance  of  the  Sun  365 

members  of  the  solar  system ;  and  Laplace  had  deduced 
a  value  of  the  solar  parallax  from  lunar  theory.  Improve-  * 
ments  in  gravitational  astronomy  and  in  observation  of  the 
planets  and  moon  during  the  present  century  have  added 
considerably  to  the  value  of  these  methods.  A  certain 
irregularity  in  the  moon's  motion  known  as  the  parallactic 
inequality,  and  another  in  the  motion  of  the  sun,  called 
the  lunar  equation,  due  to  the  displacement  of  the  earth 
by  the  attraction  of  the  moon,  alike  depend  on  the  ratio 
of  the  distances  of  the  sun  and  moon  from  the  earth ;  if 
the  amount  of  either  of  these  inequalities  can  be  observed, 
the  distance  of  the  sun  can  therefore  be  deduced,  that  of 
the  moon  being  known  with  great  accuracy.  It  was  by  a 
virtual  application  of  the  first  of  these  methods  that  Hansen 
(§206)  in  1854,  in  the  course  of  an  elaborate  investigation 
of  the  lunar  theory,  ascertained  that  the  current  value  of 
the  sun's  distance  was  decidedly  too  large,  and  Leverrier 
(§  288)  confirmed  the  correction  by  the  second  method  in 
1858. 

Again,  certain  changes  in  the  orbits  of  our  two  neigh- 
bours, Venus  and  Mars,  are  known  to  depend  upon  the 
ratio  of  the  masses  of  the  sun  and  earth,  and  can  hence 
be  connected,  by  gravitational  principles,  with  the  quantity 
sought.  Leverrier  pointed  out  in  1861  that  the  motions 
of  Venus  and  of  Mars,  like  that  of  the  moon,  were  incon- 
sistent with  the  received  estimate  of  the  sun's  distance,  and 
he  subsequently  worked  out  the  method  more  completely 
and  deduced  (1872)  values  of  the  parallax.  The  displace- 
ments to  be  observed  are  very  minute,  and  their  accurate 
determination  is  by  no  means  easy,  but  they  are  both 
secular  (chapter  XL,  §  242),  so  that  in  the  course  of  time 
they  will  be  capable  of  very  exact  measurement.  Leverrier's 
method,  which  is  even  now  a  valuable  one,  must  therefore 
almost  inevitably  outstrip  all  the  others  which  are  at  present 
known ;  it  is  difficult  to  imagine,  for  example,  that  the 
transits  of  Venus  due  in  2004  and  2012  will  have  any 
value  for  the  purpose  of  the  determination  of  the  sun's 
distance. 

283.  One  other  method,  in  two  slightly  different  forms, 
has  become  available  during  this  century.  The  displace- 
ment of  a  star  by  aberration  (chapter  x.,  §210)  depends 


366  A  Short  History  of  Astronomy          [CH.  xin. 

upon  the  ratio  of  the  velocity  of  light  to  that  of  the  earth 
in  its  orbit  round  the  sun ;  and  observations  of  Jupiter's 
satellites  after  the  manner  of  Roemer  (chapter  vin.,  §  162) 
give  the  light-equation,  or  time  occupied  by  light  in 
travelling  from  the  sun  to  the  earth.  Either  of  these 
astronomical  quantities — of  which  aberration  is  the  more 
accurately  known — can  be  used  to  determine  the  velocity 
of  light  when  the  dimensions  of  the  solar  system  are  known, 
or  vice  versa.  No  independent  method  of  determining  the 
velocity  of  light  was  known  until  1849,  when  Hippolyte 
Fizeau  (1819-1896)  invented  and  successfully  carried  out 
a  laboratory  method. 

New  methods  have  been  devised  since,  and  three  com- 
paratively recent  series  of  experiments,  by  M.  Cornu  in 
France  {1874  and  1876)  and  by  Dr.  Michelson  (1879) 
and  Professor  Newcomb  (1880-82)  in  the  United  States, 
agreeing  closely  with  one  another,  combine  to  fix  the  velocity 
of  light  at  very  nearly  186,300  miles  (299,800  kilometres) 
per  second ;  the  solar  parallax  resulting  from  this  by  means 
of  aberration  is  very  nearly  8"*8.* 

284.  Encke's  value  of  the  sun's  parallax,  8" "571,  deduced 
from  the  transits  of  Venus  (chapter  x.,  §  227)  in  1761  and 
1769,  and  published  in  1835,  corresponding  to  a  distance 
of  about  95,000,000  miles,  was  generally  accepted  till  past 
the  middle  of  the  century.  Then  the  gravitational  methods 
of  Harisen  and  Leverrier,  the  earlier  determinations  of  the 
velocity  of  light,  and  the  observations  made  at  the  opposition 
of  Mars  in  1862,  all  pointed  to  a  considerably  larger  value 
of  the  parallax;  a  fresh  examination  of  the  i8th  century 
observations  shewed  that  larger  values  than  Encke's  could 
easily  be  deduced  from  them;  and  for  some  time — from 
about  1860  onwards — a  parallax  of  nearly  8"'95,  correspond- 
ing to  a  distance  of  rather  more  than  91,000,000  miles,  was 
in  common  use.  Various  small  errors  in  the  new  methods 
were,  however,  detected,  and  the  most  probable  value  of  the 
parallax  has  again  increased.  Three  of  the  most  reliable 
methods,  the  diurnal  method  as  applied  to  Mars  in  1877, 
the  same  applied  to  the  minor  planets  in  1888-89,  and 

*  Newcomb's  velocity  of  light  and  Nyren's  constant  of  aberration 
(2o"'492i)  give  8"794;  Struve's  constant  of  aberration  (2O"'445), 
Loewy's  (2o"'447)i  and  Hall's  (2o"'454)  each  give  8"'8l. 


$$284—286]      Solar  Parallax:    Variation  of  Latitude        367 

aberration,  unite  in  giving  values  not  differing  from  8"'8o 
by  more  than  two  or  three  hundredths  of  a  second.  The 
results  of  the  last  transits  of  Venus,  the  publication  and 
discussion  of  which  have  been  spread  over  a  good  many 
years,  point  to  a  somewhat  larger  value  of  the  parallax. 
Most  astronomers  appear  to  agree  that  a  parallax  of  8" "8, 
corresponding  to  a  distance  of  rather  less  than  93,000,000 
miles,  represents  fairly  the  available  data. 

285.  The   minute   accuracy   of  modern   observations   is 
well  illustrated  by  the  recent  discovery  of  a  variation   in 
the  latitude  of  several  observatories.     Observations  taken  at 
Berlin  in  1884-85  indicated  a  minute  variation  in  the  latitude; 
special   series   of  observations  to   verify  this  were  set   on 
foot  in  several  European  observatories,  and  subsequently  at 
Honolulu  and  at  Cordoba.    A  periodic  alteration  in  latitude 
amounting  to  about  |"  emerged  as  the  result.     Latitude 
being  defined  (chapter  x.,  §  221)  as  the  angle  which  the 
vertical   at   any  place   makes  with   the   equator,  which   is 
the  same  as  the  elevation  of  the  pole  above  the  horizon, 
is  consequently  altered  by  any  change  in  the  equator,  and 
therefore  by  an  alteration  in  the  position  of  the  earth's  poles 
or  the  ends  of  the.  axis  about  which  it  rotates. 

Dr.  S.  C.  Chandler  succeeded  (1891  and  subsequently) 
in  shewing  that  the  observations  in  question  could  be  in 
great  part  explained  by  supposing  the  earth's  axis  to  undergo 
a  minute  change  of  position  in  such  a  way  that  either  pole 
of  the  earth  describes  a  circuit  round  its  mean  position  in 
about  427  days,  never  deviating  more  than  some  30  feet 
from  it.  It  is  well  known  from  dynamical  theory  that  a 
rotating  body  such  as  the  earth  can  be  displaced  in  this 
manner,  but  that  if  the  earth  were  perfectly  rigid  the  period 
should  be  306  days  instead  of  427.  The  discrepancy 
between  the  two  numbers  has  been  ingeniously  used  as  a 
test  of  the  extent  to  which  the  earth  is  capable  of  yielding 
— like  an  elastic  solid — to  the  various  forces  which  tend  to 
strain  it. 

286.  All  the  great  problems  of  gravitational  astronomy 
have   been   rediscussed  since  Laplace's   time,  and  further 
steps  taken  towards  their  solution, 

Laplace's  treatment  of  the  lunar  theory  was  first  developed 
by  Marie  Charles  Theodore  Damoiseau  (1768-1846),  whose. 


368  A  Short  History  of  Astronomy          \CH.  xill. 

Tables  de  la  Lune  (1824  and  1828)  were  for  some  time  in 
general  use. 

Some  special  problems  of  both  lunar  and  planetary  theory 
were  dealt  with  by  Simeon  Denis  Poisson  (1781-1840),  who 
is,  however,  better  known  as  a  writer  on  other  branches  of 
mathematical  physics  than  as  an  astronomer.  A  very 
elaborate  and  detailed  theory  of  the  moon,  investigated  by 
the  general  methods  of  Laplace,  was  published  by  Giovanni 
Antonio  Amadeo  Plana  (1781-1869)  in  1832,  but  unac- 
companied by  tables.  A  general  treatment  of  both  lunar 
and  planetary  theories,  the  most  complete  that  had  appeared 
up  to  that  time,  by  Philippe  Gustave  Doulcet  de  Pontecoulant 
(1795-1874),  appeared  in  1846,  with  the  title  Theorie 
Analytique  du  Systeme  du  Monde  ;  and  an  incomplete 
lunar  theory  similar  to  his  was  published  by  John  William 
Lubbock  (1803-1865)  in  1830-34. 

A  great  advance  in  lunar  theory  was  made  by  Peter 
Andreas  Hansen  (1795-1874)  of  Gotha,  who  published  in 
1838  and  1862-64  the  treatises  commonly  known  respectively 
as  the  Fundamenta  *  and  the  Darlegung^  and  produced 
in  1857  tables  of  the  moon's  motion  of  such  accuracy  that 
the  discrepancies  between  the  tables  and  observations  in 
the  century  1750-1850  were  never  greater  than  i"  or  2". 
These  tables  were  at  once  used  for  the  calculation  of  the 
Nautical  Almanac  and  other  periodicals  of  the  same  kind, 
and  with  some  modifications  have  remained  in  use  up  to 
the  present  day. 

A  completely  new  lunar  theory — of  great  mathematical 
interest  and  of  equal  complexity — was  published  by  Charles 
Delaunay  (1816-1872)  in  1860  and  1867.  Unfortunately 
the  author  died  before  he  was  able  to  work  out  the 
corresponding  tables. 

Professor  Newcomb  of  Washington  (§  283)  has  rendered 
valuable  services  to  lunar  theory — as  to  other  branches  of 
astronomy — by  a  number  of  delicate  and  intricate  calcula- 
tions, the  best  known  being  his  comparison  of  Hansen's  tables 
with  observation  and  consequent  corrections  of  the  tables. 

*  Fundamenta  Nova  Investigationis  Orbitae  Verae  quam  Luna 
perlustrat. 

f  Darlegung  der  theoretischen  Berechnung  der  in  den  Mondtafeln 
angewandten  Storungen. 


§  287]  Lunar  Theory  369 

New  methods  of  dealing  with  lunar  theory  were  devised 
by  the  late  Professor  John  Couch  Adams  of  Cambridge 
(1819-1892),  and  similar  methods  have  been  developed  by 
Dr.  G.  W.  Hill  of  Washington ;  so  far  they  have  not  been 
worked  out  in  detail  in  such  a  way  as  to  be  available  for 
the  calculation  of  tables,  and  their  interest  seems  to  be 
at  present  mathematical  rather  than  practical;  but  the 
necessary  detailed  work  is  now  in  progress,  and  these  and 
allied  methods  may  be  expected  to  lead  to  a  considerable 
diminution  of  the  present  excessive  intricacy  of  lunar 
theory. 

287.  One  special  point  in  lunar  theory  may  be  worth 
mentioning.  The  secular  acceleration  of  the  moon's  mean 
motion  which  had  perplexed  astronomers  since  its  first 
discovery  by  Halley  (chapter  x.,  §  201)  had,  as  we  have 
seen  (chapter  XL,  §  240),  received  an  explanation  in  1787 
at  the  hands  of  Laplace.  Adams,  on  going  through  the 
calculation,  found  that  some  quantities  omitted  by  Laplace 
as  unimportant  had  in  reality  a  very  sensible  effect  on  the 
result,  so  that  a  certain  quantity  expressing  the  rate  of 
increase  of  the  moon's  motion  came  out  to  be  between 
5"  and  6",  instead  of  being  about  10",  as  Laplace  had  found 
and  as  observation  required.  The  correction  was  disputed 
at  first  by  several  of  the  leading  experts,  but  was  confirmed 
independently  by  Delaunay  and  is  now  accepted.  The 
moon  appears  in  consequence  to  have  a  certain  very  minute 
increase  in  speed  for  which  the  theory  of  gravitation  affords 
no  explanation.  An  ingenious  though  by  no  means  certain 
explanation  was  suggested  by  Delaunay  in  1865.  It  had 
been  noticed  by  Kant  that  tidal  friction— that  is,  the  friction 
set  up  between  the  solid  earth  and  the  ocean  as  the  result 
of  the  tidal  motion  of  the  latter — would  have  the  effect  of 
Checking  to  some  extent  the  rotation  of  the  earth  ;  but  as 
;he  effect  seemed  to  be  excessively  minute  and  incapable 
of  precise  calculation  it  was  generally  ignored.  An  attempt 
to  calculate  its  amount  was,  however,  made  in  1853  by 
William  Ferrel,  who  also  pointed  out  that,  as  the  period 
of  the  earth's  rotation — the  day — is  our  fundamental  unit 
of  time,  a  reduction  of  the  earth's  rate  of  rotation  involves 
the  lengthening  of  our  unit  of  time,  and  consequently  pro- 
duces an  apparent  increase  of  speed  in  all  other  motions 

24. 


370  A  Short  History  of  Astronomy          [CH.  xni. 

measured  in  terms  of  this  unit.  Delaunay,  working  inde- 
pendently, arrived  at  like  conclusions,  and  shewed  that  tidal 
friction  might  thus  be  capable  of  producing  just  such  an 
alteration  in  the  moon's  motion  as  had  to  be  explained ;  if 
this  explanation  were  accepted  the  observed  motion  of  the 
moon  would  give  a  measure  of  the  effect  of  tidal  friction. 
The  minuteness  of  the  quantities  involved  is  shewn  by 
the  fact  that  an  alteration  in  the  earth's  rotation  equivalent 
to  the  lengthening  of  the  day  by  T^  second  in  10,000  years 
is  sufficient  to  explain  the  acceleration  in  question.  More- 
over it  is  by  no  means  certain  that  the  usual  estimate  of 
the  amount  of  this  acceleration — based  as  it  is  in  part  on 
ancient  eclipse  observations — is  correct,  and  even  then  a 
part  of  it  may  conceivably  be  due  to  some  indirect  effect 
of  gravitation  even  more  obscure  than  that  detected  by 
Laplace,  or  to  some  other  cause  hitherto  unsuspected. 

288.  Most  of  the  writers  on  lunar  theory  already  men- 
tioned have  also  made  contributions  to  various  parts  of 
planetary  theory,  but  some  of  the  most  important  advances 
in  planetary  theory  made  since  the  death  of  Laplace  have 
been  due  to  the  French  mathematician  Urbain  Jean  Joseph 
Leverrier  (1811-1877),  whose  methods  of  determining  the 
distance  of  the  sun  have  been  already  referred  to  (§  282). 
His  first  important  astronomical  paper  (1839)  was  a  dis- 
cussion of  the  stability  (chapter  XL,  §  245)  of  the  system 
formed  by  the  sun  and  the  three  largest  and  most  distant 
planets  then  known,  Jupiter,  Saturn,  and  Uranus.  Subse- 
quently he  worked  out  afresh  the  theory  of  the  motion  of 
the  sun  and  of  each  of  the  principal  planets,  and  constructed 
tables  of  them,  which  at  once  superseded  earlier  ones,  and 
are  now  used  as  the  basis  of  the  chief  planetary  calculations 
in  the  Nautical  Almanac  and  most  other  astronomical 
almanacs.  Leverrier  failed  to  obtain  a  satisfactory  agree- 
ment between  observation  and  theory  in  the  case  of 
Mercury,  a  planet  which  has  always  given  great  trouble  to 
astronomers,  and  was  inclined  to  explain  the  discrepancies 
as  due  to  the  influence  either  of  a  planet  revolving  between 
Mercury  and  the  sun  or  of  a  number  of  smaller  bodies 
analogous  to  the  minor  planets  (§  294). 

Researches  of  a  more  abstract  character,  connecting 
planetary  theory  with  some  of  the  most  recent  advances 


§*  288,  289]  Planetary  Theory  371 

in  pure  mathematics,  have  been  carried  out  by  Hugo  Gylden 
(1841-1896),  while  one  of  the  most  eminent  pure  mathe- 
maticians of  the  day,  M.  Henri  Poincare  of  Paris,  has 
recently  turned  his  attention  to  astronomy,  and  is  engaged 
in  investigations  which,  though  they  have  at  present  but 
little  bearing  on  practical  astronomy,  seem  likely  to  throw 
important  light  on  some  of  the  general  problems  of  celestial 
mechanics. 

-  289.  One  memorable  triumph  of  gravitational  astronomy, 
the  discovery  of  Neptune,  has  been  described  so  often  and 
so  fully  elsewhere  *  that  a  very  brief  account  will  suffice 
here.  Soon  after  the  discovery  of  Uranus  (chapter  xn., 
§  253)  it  was  found  that  the  planet  had  evidently  been 
observed,  though  not  recognised  as  a  planet,  as  early  as 
1690,  and  on  several  occasions  afterwards. 

When  the  first  attempts  were  made  to  compute  its  orbit 
carefully,  it  was  found  impossible  satisfactorily  to  reconcile 
the  earlier  with  the  later  observations,  and  in  Bouvard's 
tables  (chapter  XL,  §  247,  note)  published  in  1821  the 
earlier  observations  were  rejected.  But  even  this  drastic 
measure  did  not  cure  the  evil ;  discrepancies  between  the 
observed  and  calculated  places  soon  appeared  and  increased 
year  by  year.  Several  explanations  were  proposed,  and 
more  than  one  astronomer  threw  out  the  suggestion  that 
the  irregularities  might  be  due  to  the  attraction  of  a  hitherto 
unknown  planet.  The  first  serious  attempt  to  deduce  from 
the  irregularities  in  the  motion  of  Uranus  the  position  of 
this  hypothetical  body  was  made  by  Adams  immediately 
after  taking  his  degree  (1843).  By  October  1845  ne  na& 
succeeded  in  constructing  an  orbit  for  the  new  planet,  and 
in  assigning  for  it  a  position  differing  (as  we  now  know)  by 
less  than  2°  (four  times  the  diameter  of  the  full  moon)  from 
its  actual  position.  No  telescopic  search  for  it  was,  how- 
ever, undertaken.  Meanwhile,  Leverrier  had  independently 
taken  up  the  inquiry,  and  by  August  3ist,  1846,  he,  like 
Adams,  had  succeeded  in  determining  the  orbit  and  the 
position  of  the  disturbing  body.  On  the  23rd  of  the  follow- 

*  E.g.  in  Grant's  History  of  Physical  Astronomy,  Herschel's  Out- 
lines of  Astronomy,  Miss  Clarke's  History  of  Astronomy  in  the 
Nineteenth  Century,  and  the  memoir  by  Dr.  Glaisher  prefixed  to  the 
first  volume  of  Adams's  Collected  Papers. 


372  A  Short  History  of  Astronomy          [CH.  xm. 

ing  month  Dr.  Galle  of  the  Berlin  Observatory  received 
from  Leverrier  a  request  to  search  for  it,  and  on  the  same 
evening  found  close  to  the  position  given  by  Leverrier  a 
strange  body  shewing  a  small  planetary  disc,  which  was 
soon  recognised  as  a  new  planet,  known  now  as  Neptune. 

It  may  be  worth  while  noticing  that  the  error  in  the 
motion  of  Uranus  which  led  to  this  remarkable  discovery 
never  exceeded  2',  a  quantity  imperceptible  to  the  ordinary 
eye ;  so  that  if  two  stars  were  side  by  side  in  the  sky,  one 
in  the  true  position  of  Uranus  and  one  in  the  calculated 
position  as  given  by  Bouvard's  tables,  an  observer  of 
ordinary  eyesight  would  see  one  star  only. 

290.  The  lunar  tables  of  Hansen  and  Professor  Newcomb, 
and   the    planetary   and    solar    tables   of    Leverrier,   Pro- 
fessor Newcomb,  and  Dr.   Hill,  represent  the  motions  of 
the  bodies  dealt  with  much  more  accurately  than  the  corre- 
sponding tables  based  on  Laplace's  work,  just  as  these  were 
in  turn  much  more  accurate  than  those  of  Euler,  Clairaut, 
and  Halley.     But  the  agreement  between  theory  and  obser- 
vation is  by  no  means  perfect,  and  the  discrepancies  are  in 
many  cases  greater  than  can  be  explained  as  being  due  to 
the  necessary  imperfections  in  our  observations. 

The  two  most  striking  cases  are  perhaps  those  of  Mercury 
and  the  moon.  Leverrjer's  explanation  of  the  irregularities 
of  the  former  (§  288)  has  never  been  fully  justified  or 
generally  accepted ;  and  the  position  of  the  moon  as  given 
in  the  Nautical  Almanac  and  in  similar  publications  is 
calculated  by  means  of  certain  corrections  to  Hansen's 
tables  which  were  deduced  by  Professor  Newcomb  from 
observation  and  have  no  justification  in  the  theory  of 
gravitation. 

291.  The   calculation  of  the   paths  of  comets  has  be- 
come of  some  importance   during  this    century  owing   to 
the  discovery  of  a  number  of  comets  revolving  round  the 
sun    in    comparatively    short    periods.      Halley's    comet 
(chapter  XL,  §  231)  reappeared  duly  in  1835,  passing  through 
its  perihelion  within  a  few  days  of  the  times  predicted  by 
three  independent  calculators ;  and  it  may  be  confidently 
expected  again  about   1910.     Four  other  comets  are  now 
known  which,  like  Halley's,  revolve  in  elongated  elliptic 
orbits,  completing  a  revolution  in  between  70  and  80  years ; 


290—292] 


Orbits  of  Comets 


373 


two  of  these  have  been  seen  at  two  returns,  that  known  as 
Olbers's  comet  in  1815  and  1887,  and  the  Pons-Brooks 
comet  in  1 8 1 2  and  1 884.  Fourteen  other  comets  with  periods 
varying  between  35  years  (Encke's)  and  14  years  (Tuttle's), 
have  been  seen  at  more  than  one  return ;  about  a  dozen 
more  have  periods  estimated  at  less  than  a  century ;  and 
20  or  30  others  move  in  orbits  that  are  decidedly  elliptic, 
though  their  periods  are  longer  and  consequently  not  known 


1898 


FIG.  87.— The  path  of  Halley's  comet. 

with  much  certainty.  Altogether  the  paths  of  about  230 
or  240  comets  have  been  computed,  though  many  are 
highly  uncertain. 

292.  In  the  theory  of  the  tides  the  first  important  advance 
made  after  the  publication  of  the  Mecanique  Celeste  was 
the  collection  of  actual  tidal  observations  on  a  large  scale, 
their  interpretation,  and  their  comparison  with  the  results 
of  theory.  The  pioneers  in  this  direction  were  Lubbock 
(§  286),  who  presented  a  series  of  papers  on  the  subject 


374  A  Short  History  of  Astronomy  [Cn.  xin. 

to  the  Royal  Society  in  1830-37,  and  William  Whewell 
(1794-1866),  whose  papers  on  the  subject  appeared  between 
1833  and  1851.  Airy  (§  281),  then  Astronomer  Royal, 
also  published  in  1845  an  important  treatise  dealing  with 
the  whole  subject,  and  discussing  in  detail  the  theory  of 
tides  in  bodies  of  water  of  limited  extent  and  special  form. 
The  analysis  of  tidal  observations,  a  large  number  of  which 
taken  fro  MI  all  parts  of  the  world  are  now  available,  has. 
subsequently  been  carried  much  further  by  new  methods 
due  to  Lord  Kelvin  and  Professor  G.  If.  Darwin.  A 
large  quantity  of  information  is  thus  available  as  to  the 
way  in  which  tides  actually  vary  in  different  places  and 
according  to  different  positions  of  the  sun  and  moor. 

Of  late  years  a  good  deal  of  attention  has  been  paid  to 
the  effect  of  the  attraction  of  the  sun  and  moon  in  producing 
alterations — analogous  to  oceanic  tides — in  the  earth  itself. 
No  body  is  perfectly  rigid,  and  the  forces  in  question  must 
therefore  produce  some  tidal  effect.  The  problem  was  first 
investigated  by  Lord  Kelvin  in  1863,  subsequently  by 
Professor  Darwin  and  others.  Although  definite  numerical 
results  are  hardly  attainable  as  yet,  the  work  so  far  carried 
out  points  to  the  comparative  smallness  of  these  bodily 
tides  and  the  consequent  great  rigidity  of  the  earth,  a  result 
of  interest  in  connection  with  geological  inquiries  into  the 
nature  of  the  interior  of  the  earth. 

Some  speculations  connected  with  tidal  friction  are 
referred  to  elsewhere  (§320). 

293.  The  series  of  propositions  as  to  the  stability  of 
the  solar  system  established  by  Lagrange  and  Laplace 
(chapter  XL,  §§  244,  245),  regarded  as  abstract  propositions 
mathematically  deducible  from  certain  definite  assumptions, 
have  been  confirmed  and  extended  by  later  mathematicians 
such  as  Poisson  and  Leverrier ;  but  their  claim  to  give 
information  as  to  the  condition  of  the  actual  solar  system 
at  an  indefinitely  distant  future  time  receives  much  less 
assent  now  than  formerly.  The  general  trend  of  scientific 
thought  has  been  towards  the  fuller  recognition  of  the 
merely  aDproximate  and  probable  character  of  even  the  best 
ascertained  portions  of  our  knowledge  ;  "  exact,"  "always," 
and  "certain"  are  words  which  are  disappearing  from  the 
scientific  vocabulary,  except  as  convenient  abbreviations. 


§  293]          Tides:  the  Stability  of  the  Solar  System  375 

Propositions  which  profess,  to  be — or  are  commonly  inter- 
preted as  being — "exact"  and  valid  throughout  all  future 
time  are  consequently  regarded  with  considerable  distrust, 
unless  they  are  clearly  mere  abstractions. 

In  the  case  of  the  particular  propositions  in  question  the 
progress  of  astronomy  and  physics  has  thrown  a  good  deal 
of  emphasis  on  some  of  the  points  in  which  the  assumptions 
required  by  Lagrange  and  Laplace  are  not  satisfied  by  the 
actual  solar  system. 

It  was  assumed  for  the  purposes  of  the  stability  theorems 
that  the  bodies  of  the  solar  system  are  perfectly  rigid ;  in 
other  words,  the  motions  relative  to  one  another  of  the  parts 
of  any  one  body  were  ignored.  Both  the  ordinary  tides  of 
the  ocean  and  the  bodily  tides  to  which  modern  research 
has  called  attention'  were  therefore  left  out  of  account. 
Tidal  friction,  though  at  present  very  minute  in  amount 
(§  287),  differs  essentially  from  the  perturbations  which 
form  the  main  subject-matter  of  gravitational  astronomy, 
inasmuch  as  its  action  is  irreversible.  •  The  stability  theorems 
shewed  in  effect  that  the  ordinary  perturbations  produced 
effects  which  sooner  or  later  compensated  one  another,  so 
that  if  a  particular  motion  was  accelerated  at  one  time  it 
would  be  retarded  at  another ;  but  this  is  not  the  case  with 
tidal  friction.  Tidal  action  between  the  earth  and  the 
moon,  for  example,  gradually  lengthens  both  the  day  and  the 
month,  and  increases  the  distance  between  the  earth  and 
the  moon.  Solar  tidal  action  has  a  similar  though  smaller 
effect  on  the  sun  and  earth.  The  effect  in  each  case — as 
far  as  we  can  measure  it  at  all — seems  to  be  minute  almost 
beyond  imagination,  but  there  is  no  compensating  action 
tending  at  any  time  to  reverse  the  process.  And  on  the 
whole  the  energy  of  the  bodies  concerned  is  thereby  lessened. 
Again,  modern  theories  of  light  and  electricity  require  space 
to  be  filled  with  an  "ether"  capable  of  transmitting  certain 
waves ;  and  although  there  is  no  direct  evidence  that  it  in 
any  way  affects  the  motions  of  earth  or  planets,  it  is  difficult 
to  imagine  a  medium  so  different  from  all  known  forms  of 
ordinary  matter  as  to  offer  no  resistance  to  a  body  moving 
through  it.  Such  resistance  would  have  the  effect  of  slowly 
bringing  the  members  of  the  solar  system  nearer  to  the  sun, 
and  gradually  diminishing  their  times  of  revolution  round 


376  A  Short  History  of  Astronomy          [CH.  xin 

it.  This  is  again  an  irreversible  tendency  for  which  we 
know  of  no  compensation. 

In  fact,  from  the  point  of  view  which  Lagrange  and 
Laplace  occupied,  the  solar  system  appeared  like  a  clock 
which,  though  not  going  quite  regularly,  but  occasionally 
gaining  and  occasionally  losing,  nevertheless  required  no 
winding  up ;  whereas  modern  research  emphasises  the 
analogy  to  a  clock  which  after  all  is  running  down,  though 
at  an  excessively  slow  rate.  Modern  study  of  the  sun's 
heat  (§  319)  also  indicates  an  irreversible  tendency  towards 
the  "  running  down  "  of  the  solar  system  in  another  way. 

294.  Our  account  of  modern  descriptive  astronomy  may 
conveniently  begin  with  planetary  discoveries. 

The  first  day  of  the  igth  century  was  marked  by  the 
discovery  of  a  new  planet,  known  as  Ceres.  It  was  seen 
by  Giuseppe  Piazzi  (1746-1826)  as  a  strange  star  in  a 
region  of  the  sky  which  he  was  engaged  in  mapping,  and 
soon  recognised  by  its  motion  as  a  planet.  Its  orbit — 
first  calculated  by  Gauss  (§  276) — shewed  it  to  belong 
to  the  space  between  Mars  and  Jupiter,  which  had  been 
noted  since  the  time  of  Kepler  as  abnormally  large.  That 
a  planet  should  be  found  in  this  region  was  therefore 
no  great  surprise  ;  but  the  discovery  by  Heinrich  Olbers 
(1758-1840),  scarcely  a  year  later  (March.  1802),  of  a  second 
body  (Pallas),  revolving  at  nearly  the  same  distance  from 
the  sun,  was  wholly  unexpected,  and  revealed  an  entirely 
new  planetary  arrangement.  It  was  an  obvious  con- 
jecture that  if  there  was  room  for  two  planets  there  was 
room  for  more,  and  two  fresh  discoveries  (Juno  in  1804, 
Vesta  in  1807)  soon  followed. 

The  new  bodies  were  very  much  smaller  than  any  of 
the  other  planets,  and,  so  far  from  readily  shewing  a 
planetary  disc  like  their  neighbours  Mars  and  Jupiter, 
were  barely  distinguishable  in  appearance  from  fixed  stars, 
except  in  the  most  powerful  telescopes  of  the  time ;  hence 
the  name  asteroid  (suggested  by  William  Herschel)  or 
minor  planet  has  been  generally  employed  to  distinguish 
them  from  the  other  planets.  Herschel  attempted  to 
measure  their  size,  and  estimated  the  diameter  of  the  largest 
at  under  200  miles  (that  of  Mercury,  the  smallest  of  the 
ordinary  planets,  being  3000),  but  the  problem  was  in  reality 


FIG.  88. — Photographic  trail  of  a  minor  planet. 

[To  face  p.  377. 


$  2Q4]  The  Minor  Planets  377 

too  difficult  even  for  his  unrivalled  powers  of  observation. 
The  minor  planets  were  also  found  to  be  remarkable  for 
the  great  inclination  and  eccentricity  of  some  of  the  orbits  ; 
the  path  of  Pallas,  for  example,  makes  an  angle  of  35°  with 
the  ecliptic,  and  its  eccentricity  is  |,  so  that  its  least  dis- 
tance from  the  sun  is  not  much  more  than  half  its  greatest 
distance.  These  characteristics  suggested  to  Olbers  that 
the  minor  planets  were  in  reality  fragments  of  a  primeval 
planet  of  moderate  dimensions  which  had  been  blown 
to  pieces,  and  the  theory,  which  fitted  most  of  the  facts 
then  known,  was  received  with  great  favour  in  an  age 
when  "  catastrophes "  were  still  in  fashion  as  scientific 
explanations. 

The  four  minor  planets  named  were  for  nearly  40  years 
the  only  ones  known ;  then  a  fifth  was  discovered  in 
1845  by  Karl  Ludwig  Hencke  (1793-1866)  after  15  years 
of  search.  Two  more  were  found  in  1847,  another  in 
1848,  and  the  number  has  gone  on  steadily  increasing 
ever  since.  The  process  of  discovery  has  been  very  much 
facilitated  by  improvements  in  star  maps,  and  latterly  by 
the  introduction  of  photography.  In  this  last  method, 
first  used  by  Dr.  Max  Wolf  of  Heidelberg  in  1891,  a 
photographic  plate  is  exposed  for  some  hours ;  any  planet 
present  in  the  region  of  the  sky  photographed,  having 
moved  sensibly  relatively  to  the  stars  in  this  period,  is  thus 
detected  by  the  trail  which  its  image  leaves  on  the  plate. 
The  annexed  figure  shews  (near  the  centre)  the  trail  of  the 
minor  planet  Svea,  discovered  by  Dr.  Wolf  on  March 
2ist,  1892. 

At  the  end  of  1897  no  less  than  432  minor  planets  were 
known,  of  which  92  had  been  discovered  by  a  single 
observer,  M.  Chariots  of  Nice,  and  only  nine  less  by 
Professor  Pa  lisa  of  Vienna. 

The  paths  of  the  minor  planets  practically  occupy  the 
whole  region  between  the  paths  of  Mars  and  Jupiter, 
though  few  are  near  the  boundaries ;  no  orbit  is  more 
inclined  to  the  ecliptic  than  that  of  Pallas,"  and  the 
eccentricities  range  from  almost  zero  up  to  about  3. 

Fig.  89  shews  the  orbits  of  the  first  two  minor  planets 
discovered,  as  well  as  of  No.  323  (J5rucia)y  which  comes 
nearest  to  the  sun,  and  of  No.  361  (not  yet  named), 


378 


A  Short  History  of  Astronomy  [CH.  xin. 


which  goes  farthest  from  it.  All  the  orbits  are  described 
in  the  standard,  or  west  to  east,  direction.  The  most 
interesting  characteristic  in  the  distribution  of  the  minor 
planets,  first  noted  in  1866  by  Daniel Kir ~kwood(\^\ 5-1895), 
is  the  existence  of  comparatively  clear  spaces  in  the  regions 
where  the  disturbing  action  of  Jupiter  would  by  Lagrange's 


FIG.  89. — Paths  of  minor  planets. 

principle  (chapter  XL,  §  243)  be  most  effective  :  for  instance, 
at  a  distance  from  the  sun  about  five-eighths  that  of  Jupiter, 
a  planet  w*ould  by  Kepler's  law  revolve  exactly  twice  as  fast 
as  Jupiter ;  and  accordingly  there  is  a  gap  among  the  minor 
planets  at  about  this  distance. 

Estimates  of  the  sizes  'and  masses  of  the  minor  planets 
are  still   very  uncertain.      The   first  direct   measurements 


294] 


The  Minor  Planets 


379 


of  any  of  the  discs  which  seem  reliable  are  those  of 
Professor  E.  E.  Barnard^  made  at  the  Lick  Observatory 
in  1894  and  1895  ;  according  to  these  the  three  largest 
minor  planets,  Ceres,  Pallas,  and  Vesta,  have  diameters 
of  nearly  500  miles,  about  300  and  about  250  miles 
respectively.  Their  sizes  compared  with  the  moon  are 
shewn  on  the  diagram  (fig.  90).  An  alternative  method — 
the  only  one  available  except  for  a  few  of  the  very  largest 


FIG.  90. — Comparative  sizes  of  three  minor  planets  and  the  moon. 

of  the  minor  planets — is  to  measure  the  amount  of  light  re- 
ceived, and  hence  to  deduce  the  size,  on  the  assumption  that 
the  reflective  power  is  the  same  as  that  of  some  known  planet. 
This  method  gives  diameters  of  about  300  miles  for  the 
brightest  and  of  about  a  dozen  miles  for  the  faintest  known. 
Leverrier  calculated  from  the  perturbations  of  Mars  that 
the  total  mass  of  all  known  or  unknown  bodies  between 
Mars  and  Jupiter  could  not  exceed  a  fourth  that  of  the  earth  ; 
but  such  knowledge  of  the  sizes  as  we  can  derive  from 


380 


A  Short  History  of  Astronomy  [CH.  xm. 


light-observations  seems  to  indicate  that  the  total  mass  of 
those  at  present  known  is  many  hundred  times  less  than 
this  limit. 

295.  Neptune  and  the  minor  planets  are  the  only  planets 
which  have  been  discovered  during  this  century,  but  several 
satellites  have  been  added  to  our  system. 

Barely  a  fortnight  after  the  discovery  of  Neptune  (1846) 


JAPCTUS 


•  lENCELADUS    \ 
-DIONE     !       .'HYPEH,ON 


FIG.  91. — Saturn  and  its  system. 

a  satellite  was  detected  by  William  Lassell  (1799-1880) 
at  Liverpool.  Like  the  satellites  of  Uranus,  this  revolves 
round  its  primary  from  east  to  west — that  is,  in  the  direction 
contrary  to  that  of  all  the  other  known  motions  of  the  solar 
system  (certain  long-period  comets  not  being  counted). 

Two  years  later  (September  i6th,  1848)  William  Cranch 
Bond  (1789-1859)   discovered,    at   the   Harvard    College 


§  295l  New  Satellites  381 

Observatory,  an  eighth  satellite  of  Saturn,  called  Hyperion, 
which  was  detected  independently  by  Lassell  two  days 
afterwards.  In  the  following  year  Bond  discovered  that 
Saturn  was  accompanied  by  a  third  comparatively  dark  ring 
— now  commonly  known  as  the  crape  ring — lying  imme- 
diately inside  the  bright  rings  (see  fig.  95);  and  the 
discovery  was  made  independently  a  fortnight  later  by 


\ 


\ 


\ 

\ 
\ 
i 
i 
\ 
\ 
i 
t 
i 
t 

0PHOB08  DE1MOS* 

i 
I 
i 
I 

t 
I 

--,. 

*'-«..  _.^  __,--" 

FIG.  92. — Mars  and  its  satellites. 

William  Rutter  Dawes  (1799-1868)  in  England.  Lassell 
discovered  in  1851  two  new  satellites  of  Uranus,  making 
a  total  of  four  belonging  to  that  planet.  The  next  dis- 
coveries were  those  of  two  satellites  of  Mars,  known  as 
Deimos  and  Phobos,  by  Professor  Asaph  Hall  of  Washington 
on  August  nth  and  i7th,  1877.  These  are  remarkable 
chiefly  for  their  close  proximity  to  Mars  and  their  extremely 
rapid  motion,  the  nearer  one  revolving  more  rapidly  than 


382  A  Short  History  of  Astronomy          [CH.  xin. 

Mars  rotates,  so  that  to  the  Martians  it  must  rise  in  the 
west  and  set  in  the  east.  Lastly,  Jupiter's  system  received 
an  addition  after  nearly  three  centuries  by  Professor  Barnard's 
discovery  at  the  Lick  Observatory  (September  9th,  1892)  of 


'•".,- .,\  -\ 

.'  .  »  • 


\ 


\  N  '  t 


• 


' 


iiv 

i 
i 


FIG.  93. — Jupiter  and  its  satellites. 

an  extremely  faint  fifth  satellite,  a  good  deal  nearer  to  Jupiter 
than  the  nearest  of  Galilei's  satellites  (chapter  vi.,  §  121). 

296.  The  surfaces  of  the  various  planets  and  satellites 
have  been  watched  with  the  utmost  care  by  an  army  of 
observers,  but  the  observations  have  to  a  large  extent 
remained  without  satisfactory  interpretation,  and  little  is 
known  of  the  structure  or  physical  condition  of  the  bodies 
concerned. 

Astronomers  are  naturally  most  familiar  with  the  surface 


FIG.  94. — The  Apennines  and  adjoining  regions  ot  the  moon.     JKrom  a 

photograph  taken  at  the  Paris  Observatory.     [To  face  p.  383. 


$$  296,  297]      Satellites  of  Jupiter :  the  Moon  :  Mars          383 

of  our  nearest  neighbour,  the  moon.  The  visible  half  has 
been  elaborately  mapped,  and  the  heights  of  the  chief 
mountain  ranges  measured  by  means  of  their  shadows. 
Modern  knowledge  has  done  much  to  dispel  the  view,  held 
by  the  earlier  telescopists  and  shared  to  some  extent  even 
by  Herschel,  that  the  moon  closely  resembles  the  earth  and 
is  suitable  for  inhabitants  like  ourselves.  The  dark  spaces 
which  were  once  taken  to  be  seas  and  still  bear  that  name 
are  evidently  covered  with  dry  rock ;  and  the  craters  with 
which  the  moon  is  covered  are  all — with  one  or  two  doubt- 
ful exceptions — extinct ;  the  long  dark  lines  known  as 
rills  and  formerly  taken  for  river-beds  have  clearly  no 
water  in  them.  The  question  of  a  lunar  atmosphere  is 
more  difficult :  if  there  is  air  its  density  must  be  very  small, 
some  hundredfold  less  than  that  of  our  atmosphere  at  the 
surface  of  the  earth  ;  but  with  this  restriction  there  seems 
to  be  no  bar  to  the  existence  of  a  lunar  atmosphere  of 
considerable  extent,  and  it  is  difficult  to  explain  certain 
observations  without  assuming  the  existence  of  some  atmo- 
sphere. 

297.  Mars,  being  the  nearest  of  the  superior  planets,  is 
the  most  favourably  situated  for  observation.  The  chief 
markings  on  its  surface — provisionally  interpreted  as  being 
land  and  water — are  fairly  permanent  and  therefore 
recognisable ;  several  tolerably  consistent  maps  of  the 
surface  have  been  constructed;  and  by  observation  of 
certain  striking  features  the  rotation  period  has  been 
determined  to  a  fraction  of  a  second.  Signor  Schiaparelli 
of  Milan  detected  at  the  opposition,  of  1877  a  number  of 
intersecting  dark  lines  generally  known  as  canals,  and  as 
the  result  of  observations  made  during  the  opposition  of 
1881-82  announced  that  certain  of  them  appeared  doubled, 
two  nearly  parallel  lines  being  then  seen  instead  of  one. 
These  remarkable  observations  have  been  to  a  great  extent 
confirmed  by  other  observers,  but  remain  unexplained. 

The  visible  surfaces  of  Jupiter  and  Saturn  appear  to  be 
layers  of  clouds ;  the  low  density  of  each  planet  (1*3  and 
•7  respectively,  that  of  water  being  i  and  of  the  earth  5*5), 
the  rapid  changes  on  the  surface,  and  other  facts  indicate 
that  these  planets  are  to  a  great  extent  in  a  fluid  condition, 
and  have  a  high  temperature  at  a  very  moderate  distance 


384  A  Short  History  of  Astronomy  [CH.  xm. 

below  the  visible  surface.  The  surface  markings  are  in  each 
case  definite  enough  for  the  rotation  periods  to  be  fixed  with 
some  accuracy  ;  though  it  is  clear  in  the  case  of  Jupiter, 
and  probably  also  in  that  of  Saturn,  that — as  with  the  sun 
(§  298) — different  parts  of  the  surface  move  at  different  rates. 

Laplace  had  shewn  that  Saturn's  ring  (or  rings)  could  not 
be,  as  it  appeared,  a  uniform  solid  body ;  he  rashly  inferred 
— without  any  complete  investigation — that  it  might  be 
an  irregularly  weighted  solid  body.  The  first  important 
advance  was  made  by  James  Clerk  Maxwell  (1831-1879), 
best  known  as  a  writer  on  electricity  and  other  branches 
of  physics.  Maxwell  shewed  (1857)  that  the  rings  could 
neither  be  continuous  solid  bodies  nor  liquid,  but  that 
all  the  important  dynamical  conditions  would  be  satisfied 
if  they  were  made  up  of  a  very  large  number  of  small 
solid  bodies  revolving  independently  round  the  sun.*  The 
theory  thus  suggested  on  mathematical  grounds  has  re- 
ceived a  good  deal  of  support  from  telescopic  evidence. 
The  rings  thus  bear  to  Saturn  a  relation  having  some 
analogy  to  that  which  the  minor  planets  bear  to  the  sun ; 
and  Kirkwood  pointed  out  in  1867  that  Cassini's  division 
between  the  two  main  rings  can  be  explained  by  the 
perturbations  due  to  certain  of  the  satellites,  just  as  the 
corresponding  gaps  in  the  minor  planets  can  be  explained 
by  the  action  of  Jupiter  (§  294). 

The  great  distance  of  Uranus  and  Neptune  naturally 
makes  the  study  of  them  difficult,  and  next  to  nothing  is 
known  of  the  appearance  or  constitution  of  either ;  their 
rotation  periods  are  wholly  uncertain. 

Mercury  and  Venus,  being  inferior  planets,  are  never  very 
far  from  the  sun  in  the  sky,  and  therefore  also  extremely 
difficult  to  observe  satisfactorily.  Various  bright  and  dark 
markings  on  their  surfaces  have  been  recorded,  but  different 
observers  give  very  different  accounts  of  them.  The  rotation 
periods  are  also  very  uncertain,  though  a  good  many  astrono- 
mers support  the  view  put  forward  by  Sig.  Schiaparelli,  in 
1882  and  1890  for  Mercury  and  Venus  respectively,  that 
each  rotates  in  a  time  equal  to  its  period  of  revolution  round 
the  sun,  and  thus  always  turns  the  same  face  towards  the 
sun.  Such  a  motion — which  is  analogous  to  that  of  the 
*  This  had  been  suggested  as  a  possibility  by  several  earlier  writers 


$  293]  Planetary  Observations :  Sun-spots  385 

moon  round  the  earth  and  of  Japetus  round  Saturn 
(chapter  xn.,  §  267) — could  be  easily  explained  as  the 
result  of  tidal  action  at  some  past  time  when  the  planets 
were  to  a  great  extent  fluid. 

298.  Telescopic  study  of  the  surface  of  the  sun  during 
the  century  has  resulted  in  an  immense  accumulation  of 
detailed  knowledge  of  peculiarities  of  the  various  markings 
on  the  surface.  The  most  interesting  results  of  a  general 
nature  are  connected  with  the  distribution  and  periodicity 
of  sun-spots.  The  earliest  telescopists  had  noticed  that  the 
number  of  spots  visible  on  the  sun  varied  from  time  to  time, 
but  no  law  of  variation  was  established  till  1851,  when  Hein- 
rich  Schwabe  of  Dessau  (1789-1 8 7 5)  published  in  Humboldt's 
Cosmos  the  results  of  observations  of  sun-spots  carried  out 
during  the  preceding  quarter  of  a  century,  shewing  that  the 
number  of  spots  visible  increased  and  decreased  in  a 
tolerably  regular  way  in  a  period  of  about  ten  years. 

Earlier  records  and  later  observations  have  confirmed 
the  general  result,  the  period  being  now  estimated  as 
slightly  over  n  years  on  the  average,  though  subject  to 
considerable  fluctuations.  A  year  later  (1852)  three  inde- 
pendent investigators,  Sir  Edward  Sabine  (1788-1883)  in 
England,  Rudolf  Wolf  (1816-1893)  and  Alfred  Gautier 
(1793-1881)  in  Switzerland,  called  attention  to  the  remark- 
able similarity  between  the  periodic  variations  of  sun-spots 
and  of  various  magnetic  disturbances  on  the  earth.  Not 
only  is  the  period  the  same,  but  it  almost  invariably  happens 
that  when  spots  are  most  numerous  on  the  sun  magnetic 
disturbances  are  most  noticeable  on  the  earth,  and  that 
similarly  the  times  of  scarcity  of  the  two  sets  of  phenomena 
coincide.  This  wholly  unexpected  and  hitherto  quite  un- 
explained relationship  has  been  confirmed  by  the  occurrence 
on  several  occasions  of  decided  magnetic  disturbances 
simultaneously  with  rapid  changes  on  the  surface  of  the  sun. 

A  long  series  of  observations  of  the  position  of  spots  on 
the  sun  undertaken  by  Richard  Christopher  Carrington 
(1826-1875)  led  to  the  first  clear  recognition  of  the  differ- 
ence in  the  rate  of  rotation  of  the  different  parts  of  the 
surface  of  the  sun,  the  period  of  rotation  being  fixed  (1859) 
at  about  25  days  at  the  equator,  and  two  and  a  half  days 
longer  half-way  between  the  equator  and  the  poles ;  while 

25 


386  A  Short  History  of  Astronomy          [CH.  xm. 

in  addition  spots  were  seen  to  have  also  independent 
"proper  motions."  Carrington  also  established  (1858)  the 
scarcity  of  spots  in  the  immediate  neighbourhood  of  the 
equator,  and  confirmed  statistically  their  prevalence  in 
the  adjacent  regions,  and  their  great  scarcity  more  than 
about  35°  from  the  equator;  and  noticed  further  certain 
regular  changes  in  the  distribution  of  spots  on  the  sun  in 
the  course  of  the  i  i-year  cycle. 

Wilson's  theory  (chapter  XH.,  §  268)  that  spots  are  de- 
pressions was  confirmed  by  an  extensive  series  of  photographs 
taken  at  Kew  in  1858-72,  shewing  a  large  preponderance 
of  cases  of  the  perspective  effect  noticed  by  him  ;  but,  on 
the  other  hand,  Mr.  F.  Howlett^  who  has  watched  the  sun 
for  some  35  years  and  made  several  thousand  drawings  of 
spots,  considers  (1894)  that  his  observations  are  decidedly 
against  Wilson's  theory.  Other  observers  are  divided  in 
opinion. 

299.  Spectrum  analysis,  which  has  played  such  an  im- 
portant part  in  recent  astronomical  work,  is  essentially  a 
method  of  ascertaining  the  nature  of  a  body  by  a  process 
of  sifting  or  analysing  into  different  components  the  light 
received  from  it. 

It  was  first  clearly  established  by  Newton,  in  1665-66 
(chapter  ix.,  §  1.68),  that  ordinary  white  light,  such  as  sun- 
light, is  composite,  and  that  by  passing  a  beam  of  sunlight 
— with  proper  precautions— through  a  glass  prism  it  can  be 
decomposed  into  light  of  different  colours ;  if  the  beam  so 
decomposed  is  received  on  a  screen,  it  produces  a  band  of 
colours  known  as  a  spectrum,  red  being  at  one  end  and 
violet  at  the  other. 

Now  according  to  modern  theories  light  consists  essen- 
tially of  a  series  of  disturbances  or  waves  transmitted  at 
extremely  short  but  regular  intervals  from  the  luminous 
object  to  the  eye,  the  medium  through  which  the  disturb- 
ances travel  being  called  ether.  The  most  important 
characteristic  distinguishing  different  kinds  of  light  is  the 
interval  of  time  or  space  between  one  wave  and  the  next, 
which  is  generally  expressed  by  means  of  wave-length,  or 
the  distance  between  any  point  of  one  wave  and  the  corre- 
sponding point  of  the  next.  Differences  in  wave-length 
shew  themselves  most  readily  as  differences  of  colour ;  so 


$  299]  Spectrum  Analysis  387 

that  light  of  a  particular  colour  found  at  a  particular  part  of 
the  spectrum  has  a  definite  wave-length.  At  the  extreme 
violet  end  of  the  spectrum,  for  example,  the  wave-length 
is  about  fifteen  millionths  of  an  inch,  at  the  red  end  it  is 
about  twice  as  great ;  from  which  it  follows  (§  283),  from 
the  known  velocity. of  light,  that  when  we  look  at  the  red  end 
of  a  spectrum  about  400  billion  waves  of  light  enter  the  eye 
per  second,  and  twice  that  number  when  we  look  at  the 
other  end.  Newton's  experiment  thus  shews  that  a  prism 
sorts  out  light  of  a  composite  nature  according  to  the  wave- 
length of  the  different  kinds  of  light  present.  The  same 
thing  can  be  done  by  substituting  for  the  prism  a  so-called 
diffraction-grating,  and  this  is  for  many  purposes  super 
seding  the  prism.  In  general  it  is  necessary,  to  ensure 
purity  in  the  spectrum  and  to  make  it  large  enough,  to 
admit  light  through  a  narrow  slit,  and  to  use  certain  lenses 
in  combination  with  one  or  more  prisms  or  a  grating  ;  and 
the  arrangement  is  such  that  the  spectrum  is  not  thrown 
on  to  a  screen,  but  either  viewed  directly  by  the  eye  or 
photographed.  The  whole  apparatus  is  known  as  a  spectro- 
scope. 

The  solar  spectrum  appeared  to  Newton  as  a  continuous 
band  of  colours  ;  but  in  1802  William  Hyde  Wollaston 
(1766-1828)  observed  certain  dark  lines  running  across  the 
spectrum,  which  he  took  to  be  the  boundaries  of  the  natural 
colours.  A  few  years  later  (1814-15)  the  great  Munich 
optician  Joseph  Fraunhofer  (1787-1826)  examined  the  sun's 
spectrum  much  more  carefully,  and  discovered  about  600 
such  dark  lines,  the  positions  of  324  of  which  he  mapped 
(see  fig.  97).  These  dark  lines  are  accordingly  known  as 
Fraunhofer  lines  :  for  purposes  of  identification  Fraunhofer 
attached  certain  letters  of  the  alphabet  to  a  few  of  the  most 
conspicuous  ;  the  rest  are  now  generally  known  by  the  wave- 
length of  the  corresponding  kind  of  light. 

It  was  also  gradually  discovered  that  dark  bands  could 
be  produced  artificially  in  spectra  by  passing  light  through 
various  coloured  substances  ;  and  that,  on  the  other  hand,  the 
spectra  of  certain  flames  were  crossed  by  various  bright  lines. 

Several  attempts  were  made  to  explain  and  to  connect 
these  various  observations,  but  the  first  satisfactory  and 
tolerably  complete  explanation  was  given  in  1859  by  Gustav 


388  A  Short  History  of  Astroncmy          [Cn.  xni. 

Robert  Kirchhoff  (1824-1887)  of  Heidelberg,  who  at  first 
worked  in  co-operation  with  the  chemist  Bunsen. 

Kirchhoff  shewed  that  a  luminous  solid  or  liquid — or, 
as  we  now  know,  a  highly  compressed  gas — gives  a  con- 
tinuous spectrum  ;  whereas  a  substance  in  the  gaseous 
state  gives  a  spectrum  consisting  of  bright  lines  (with  or 
without  a  faint  continuous  spectrum),  and  these  bright 
lines  depend  on  the  particular  substance  and  are  charac- 
teristic of  it.  Consequently  the  presence  of  a  particular 
substance  in  the  form  of  gas  in  a  hot  body  can  be  inferred 
from  the  presence  of  its  characteristic  lines  in  the  spectrum 
of  the  light.  The  dark  lines  in  the  solar  spectrum  were 
explained  by  the  fundamental  principle — often  known  as 
KirchhofFs  law — that  a  body's  capacity  for  stopping  or 
absorbing  light  of  a  particular  wave-length  is  proportional 
to  its  power,  under  like  conditions,  of  giving  out  the 
same  light.  If,  in  particular,  light  from  a  luminous  solid 
or  liquid  body,  giving  a  continuous  spectrum,  passes  through 
a  gas,  the  gas  absorbs  light  of  the  same  wave-length  as  that 
which  it  itself  gives  out :  if  the  gas  gives  out  more  light 
of  these  particular  wave-lengths  than  it  absorbs,  then  the 
spectrum  is  crossed  by  the  corresponding  bright  lines ; 
but  if  it  absorbs  more  than  it  gives  out,  then  there  is  a 
deficiency  of  light  of  these  wave-lengths  and  the  corre- 
sponding parts  of  the  spectrum  appear  dark — that  is,  the 
spectrum  is  crossed  by  dark  lines  in  the  same  position  as 
the  bright  lines  in  the  spectrum  of  the  gas  alone.  Whether 
the  gas  absorbs  more  or  less  than  it  gives  out  is  essentially 
a  question  of  temperature,  so  that  if  light  from  a  hot  solid 
or  liquid  passes  through  a  gas  at  a  higher  temperature  a 
spectrum  crossed  by  bright  lines  is  the  result,  whereas  if 
the  gas  is  cooler  than  the  body  behind  it  dark  lines  are 
seen  in  the  spectrum. 

300.  The  presence  of  the  Fraunhofer  lines  in  the 
spectrum  of  the  sun  shews  that  sunlight  comes  from  a 
hot  solid  or  liquid  body  (or  from  a  highly  compressed  gas), 
and  that  it  has  passed  through  cooler  gases  which  have 
absorbed  light  of  the  wave-lengths  corresponding  to  the 
dark  lines.  These  gases  must  be  either  round  the  sun  or 
in  our  atmosphere  ;  and  it  is  not  difficult  to  shew  that, 
although  some  of  the  Fraunhofer  lines  are  due  to  our 


§$  3°o,  so']  Spectrum  Analysis  38 

atmosphere,   the   majority    cannot   be,    and   are    therefor^ 
caused  by  gases  in  the  atmosphere  of  the  sun. 

For  example,  the  metal  sodium  when  vaporised  gives  a 
spectrum  characterised  by  two  nearly  coincident  bright 
lines  in  the  yellow  part  of  the  spectrum  ;  these  agree  in 
position  with  a  pair  of  dark  lines  (known  as  D)  in  the 
spectrum  of  the  sun  (see  fig.  97);  Kirchhoff  inferred  there- 
fore that  the  atmosphere  of  the  sun  contains  sodium.  By 
comparison  of  the  dark  lines  in  the  spectrum  of  the  sun 
with  the  bright  lines  in  the  spectra  of  metals  and  other  sub- 
stances, their  presence  or  absence  in  the  solar  atmosphere 
can  accordingly  be  ascertained.  In  the  case  of  iron — which 
has  an  extremely  complicated  spectrum — Kirchhoff  suc- 
ceeded in  identifying  60  lines  (since  increased  to  more 
than  2,000)  in  its  spectrum  with  dark  lines  in  the  spectrum 
of  the  sun.  Some  half-dozen  other  known  elements  were 
also  identified  by  Kirchhoff  in  the  sun. 

The  inquiry  into  solar  chemistry  thus  started  has  since 
been  prosecuted  with  great  zeal.  Improved  methods  and 
increased  care  have  led  to  the  construction  of  a  series  of 
maps  of  the  solar  spectrum,  beginning  with  Kirchhoff's  own, 
published  in  1861-62,  of  constantly  increasing  complexity 
and  accuracy.  Knowledge  of  the  spectra  of  the  metals  has 
also  been  greatly  extended.  At  the  present  time  between 
30  and  40  elements  have  been  identified  in  the  sun,  the 
most  interesting  besides  those  already  mentioned  being 
hydrogen,  calcium,  magnesium,  and  carbon. 

The  first  spectroscopic  work  on  the  sun  dealt  only  with 
the  light  received  from  the  sun  as  a  whole,  but  it  was  soon 
seen  that  by  throwing  an  image  of  the  sun  on  to  the  slit 
of  the  spectroscope  by  means  of  a  telescope  the  spectrum 
of  a  particular  part  of  the  sun's  surface,  such  as  a  spot  or 
a  facula,  could  be  obtained ;  and  an  immense  number  of 
observations  of  this  character  have  been  made. 

301.  Observations  of  total  eclipses  of  the  sun  have  shewn 
that  the  bright  surface  of  the  sun  as  we  ordinarily  see  it 
is  not  the  whole,  but  that  outside  this  there  is  an  envelope 
of  some  kind  too  faint  to  be  seen  ordinarily  but  becoming 
visible  when  the  intense  light  of  the  sun  itself  is  cut  off 
by  the  moon.  A  white  halo  of  considerable  extent  round 
the  eclipsed  sun,  now  called  the  corona,  is  referred  to  by 


396  A  Short  History  of  Astronomy          [CH.  xm. 

Plutarch,  and  discussed  by  Kepler  (chapter  vn.,  §  145) 
Several  i8th  century  astronomers  noticed  a  red  streak  along 
some  portion  of  the  common  edge  of  the  sun  and  moon, 
and  red  spots  or  clouds  here  and  there  (cf.  chapter  x.,  §  205). 
But  little  serious  attention  was  given  to  the  subject  till  after 
the  total  solar  eclipse  of  1842.  Observations  made  then 
and  at  the  two  following  eclipses  of  1851  and  1860,  in  the 
latter  of  which  years  photography  was  for  the  first  time 
effectively  employed,  made  it  evident  that  the  red  streak 
represented  a  continuous  envelope  of  some  kind  surrounding 
the  sun,  to  which  the  name  of  chromosphere  has  been  given, 
and  that  the  red  objects,  generally  known  as  prominences, 
were  in  general  projecting  parts  of  the  chromosphere,  though 
sometimes  detached  from  it.  At  the  eclipse  of  1868  the 
spectrum  of  the  prominences  and  the  chromosphere  was 
obtained,  and  found  to  be  one  of  bright  lines,  shewing  that 
they  consisted  of  gas.  Immediately  afterwards  M.  Janssen^ 
who  was  one  of  the  observers  of  the  eclipse,  and  Sir 
J.  Norman  Lockyer  independently  devised  a  method 
whereby  it  was  possible  to  get  the  spectrum  of  a  prominence 
at  the  edge  of  the  sun's  disc  in  ordinary  daylight,  without 
waiting  for  an  eclipse ;  and  a  modification  introduced  by 
Sir  William  Huggins  in  the  following  year  (1869)  enabled 
the  form  of  a  prominence  to  be  observed  spectroscopically. 
Recently  (1892)  Professor  G.  E.  Hale  of  Chicago  has 
succeeded  in  obtaining  by  a  photographic  process  a  repre- 
sentation of  the  whole  of  the  chromosphere  and  prominences, 
while  the  same  method  gives  also  photographs  of  faculae 
(chapter  viii.,  §  153)  on  the  visible  surface  of  the  sun. 

The  most  important  lines  ordinarily  present  in  the 
spectrum  of  the  chromosphere  are  those  of  hydrogen,  two 
lines  (H  and  K)  which  have  been  identified  with  some 
difficulty  as  belonging  to  calcium,  and  a  yellow  line  the 
substance  producing  which,  known  as  helium,  has  only 
recently  (1895)  been  discovered  on  the  earth.  But  the 
chromosphere  when  disturbed  and  many  of  the  prominences 
give  spectra  containing  a  number  of  other  lines. 

The  corona  was  for  some  time  regarded  as  of  the  nature 
of  an  optical  illusion  produced  in  the  atmosphere.  That  it 
is,  at  any  rate  in  great  part,  an  actual  appendage  of  the  sun 
was  first  established  in  1869  by  the  American  astronomers 


FIG.  98. — The  total  solar  eclipse  of  August  29th,  1886.    From  a  drawing 
based  on  photographs  by  Dr.  Schuster  and  Mr.  Maunder. 

\Toface  p.  390. 


§302]  Solar  Spedroscopy :  D applets  Principle  391 

Professor  Harkness  and  Professor  C.  A.  Young,  who  dis^ 
covered  a  bright  line — of  unknown  origin  * — in  its  spectrum, 
thus  shewing  that  it  consists  in  part  of  glowing  gas. 
Subsequent  spectroscopic  work  shews  that  its  light  is  partly 
reflected  sunlight. 

The  corona  has  been  carefully  studied  at  every  solar 
eclipse  during  the  last  30  years,  both  with  the  spectroscope 
and  with  the  telescope,  supplemented  by  photography,  and 
a  number  of  ingenious  theories  of  its  constitution  have  been 
propounded  ;  but  our  present  knowledge  of  its  nature  hardly 
goes  beyond  Professor  Young's  description  of  it  as  "  an 
inconceivably  attenuated  cloud  of  gas,  fog,  and  dust,  sur- 
rounding the  sun,  formed  and  shaped  by  solar  forces." 

302.  The  spectroscope  also  gives  information  as  to  .certain 
motions  taking  place  on  the  sun.  It  was  pointed  out  in  1842 
by  Christian  Doppler  (1803-1853),  though  in  an  imperfect 
and  partly  erroneous  way,  that  if  a  luminous  body  is 
approaching  the  observer,  or  vice  versa,  the  waves  of  light 
are  as  it  were  crowded  together  and  reach  the  eye  at  shorter 
intervals  tha-a  if  the  body  were  at  rest,  and  that  the  character 
of  the  light  is  thereby  changed.  The  colour  and  the  position 
in  the  spectrum  both  depend  on  the  interval  between  one 
wave  and  the  next,  so  that  if  a  body  giving  out  light  of  a 
particular  wave-length,  e.g.  the  blue  light  corresponding  to 
the  F  line  of  hydrogen,  is  approaching  the  observer  rapidly, 
the  line  in  the  spectrum  appears  slightly  on  one  side  of  its 
usual  position,  being  displaced  towards  the  violet  end  of 
the  spectrum ;  whereas  if  the  body  is  receding  the  line 
is,  in  the  same  way,  displaced  in  the  opposite  direction. 
This  result  is  usually  known  as  Doppler's  principle.  The 
effect  produced  can  easily  be  expressed  numerically.  If, 
for  example,  the  body  is  approaching  with  a  speed  equal 
'to  y^Vrr tnat  °f  hgnt>  then  1001  waves  enter  the  eye  or  the 
spectroscope  in  the  same  time  in  which  there  would  other- 
wise only  be  1000;  and  there  is  in  consequence  a  virtual 
shortening  of  the  wave-length  in  the  ratio  of  1001  to 
1000.  So  that  if  it  is  found  that  a  line  in  the  spectrum 
of  a  body  is  displaced  from  its  ordinary  position  in  such 

*  The  discovery  of  a  terrestrial  substance  with  this  line  in  its 
spectrum  has  been  announced  while  this  book  has  been  passing 
through  the  press. 


392  A  Short  History  of  Astronomy          [CH.  xin. 

a  way  that  its  wave-length  is  apparently  decreased  by 
Tinnr  Part>  ^  may  be  inferred  that  the  body  is  approach- 
ing with  the  speed  just  named,  or  about  186  miles  per 
second,  and  if  the  wave-length  appears  increased  by  the 
same  amount  (the  line  being  displaced  towards  the  red  end 
of  the  spectrum)  the  body  is  receding  at  the  same  rate. 

Some  of  the  earliest  observations  of  the  prominences  by 
Sir  J.  N.  Lockyer  (1868),  and  of  spots  and  other  features 
of  the  sun  by  the  same  and  other  observers,  shewed  dis- 
placements and  distortions  of  the  lines  in  the  spectrum, 
which  were  soon  seen  to  be  capable  of  interpretation  by 
this  method,  and  pointed  to  the  existence  of  violent  dis- 
turbances in  the  atmosphere  of  the  sun,  velocities  as 
great  as  300  miles  per  second  being  not  unknown.  The 
method  has  received  an  interesting  confirmation  from  obser- 
vations of  the  spectrum  of  opposite  edges  of  the  sun's  disc, 
of  which  one  is  approaching  and  the  other  receding  owing 
to  the  rotation  of  the  sun.  Professor  Duner  of  Upsala  has 
by  this  process  ascertained  (1887-89)  the  rate  of  rotation 
of  the  surface  of  the  sun  beyond  the  regions  where  spots 
exist,  and  therefore  outside  the  limits  of  observations  such 
as  Carrington's  (§  298). 

303.  The  spectroscope  tells  us  that  the  atmosphere  of 
the  sun  contains  iron  and  other  metals  in  the  form  of 
vapour;  and  the  photosphere,  which  gives  the  continuous 
part  of  the  solar  spectrum,  is  certainly  hotter.  Moreover 
everything  that  we  know  of  the  way  in  which  heat  is  com- 
municated from  one  part  of  a  body  to  another  shews  that 
the  outer  regions  of  the  sun,  from  which  heat  and  light  are 
radiating  on  a  very  large  scale,  must  be  the  coolest  parts, 
and  that  the  temperature  in  all  probability  rises  very  rapidly 
towards  the  interior.  These  facts,  coupled  with  the  low 
density  of  the  sun  (about  a  fourth  that  of  the  earth)  and 
the  violently  disturbed  condition  of  the  surface,  indicate  that 
the  bulk  of  the  interior  of  the  sun  is  an  intensely  hot  and 
highly  compressed  mass  of  gas.  Outside  this  come  in  order, 
their  respective  boundaries  and  mutual  relations  being,  how- 
ever, very  uncertain,  first  the  photosphere,  generally  regarded 
as  a  cloud-layer,  then  the  reversing  stratum  which  produces 
most  of  the  Fraunhofer  lines,  then  the  chromosphere  and 
prominences,  and  finally  the  c&rona.  Sun-spots,  faculae,  and 


«    D, 

It 

si, 


M  303, 304]  Structure  of  the  Sun :  Comets  393 

prominences  have  been  explained  in  a  variety  of  different 
ways  as  joint  results  of  solar  disturbances  of  various 
kinds ;  but  no  detailed  theory  that  has  been  given  explains 
satisfactorily  more  than  a  fraction  of  the  observed  facts 
or  commands  more  than  a  very  limited  amount  of  assent 
among  astronomical  experts. 

304.  More  than  200  comets  have  been  seen  during  the 
present  century  ;  not  only  have  the  motions  of  most  of  them 
been  observed  and  their  orbits  computed  (§  29 1 ),  but  in  a  large 
number  of  cases  the  appearance  and  structure  of  the  comet 
have  been  carefully  observed  telescopically,  while  latterly 
spectrum  analysis  and  photography  have  also  been  employed. 

Independent  lines  of  inquiry  point  to  the  extremely  un- 
substantial character  of  a  comet,  with  the  possible  exception 
of  the  bright  central  part  or  nucleus,  which  is  nearly  always 
present.  More  than  once,  as  in  1767  (chapter  XL,  §  248),  a 
comet  has  passed  close  to  some  member  of  the  solar  system, 
and  has  never  been  ascertained  to  affect  its  motion.  The 
mass  of  a  comet  is  therefore  very  small,  but  its  bulk  or 
volume,  on  the  other  hand,  is  in  general  very  great,  the  tail 
often  being  millions  of  miles  in  length  ;  so  that  the  density 
must  be  extremely  small.  Again,  stars  have  often  been  ob- 
served shining  through  a  comet's  tail  (as  shewn  in  fig.  99), 
and  even  through  the  head  at  no  great  distance  from  the 
nucleus,  their  brightness  being  only  slightly,  if  at  all,  affected. 
Twice  at  least  (1819,  1861)  the  earth  has  passed  through  a 
comet's  tail,  but  we  were  so  little  affected  that  the  fact  was 
only  discovered  by  calculations  made  after  the  event.  The 
early  observation  (chapter  in.,  §  69)  that  a  comet's  tail  points 
away  from  the  sun  has  been  abundantly  verified  ;  and  from 
this  it  follows  that  very  rapid  changes  in  the  position  of  the 
tail  must  occur  in  some  cases.  For  example,  the  comet  of 
1843  passed  very  close  to  the  sun  at  such  a  rate  that  in 
about  two  hours  it  had  passed  from  one  side  of  the  sun  to 
the  opposite ;  it  was  then  much  too  near  the  sun  to  be  seen, 
but  if  it  followed  the  ordinary  law  its  tail,  which  was  unusually 
long,  must  have  entirely  reversed  its  direction  within  this 
short  time.  It  is  difficult  to  avoid  the  inference  that  the 
tail  is  not  a  permanent  part  of  the  comet,  but  is  a  stream 
of  matter  driven  off  from  it  in  some  way  by  the  action  of 
the  sun,  and  in  this  respect  comparable  with  the  smoke 


394  d  Short  History  of  Astronomy          [CH.  xin 

issuing  from  a  chimney.  This  view  is  confirmed  by  the 
fact  that  the  tail  is  only  developed  when  the  comet 
approaches  the  sun,  a  comet  when  at  a  great  distance  from 
the  sun  appearing  usually  as  an  indistinct  patch  of  nebulous 
light,  with  perhaps  a  brighter  spot  representing  the  nucleus. 
Again,  if  the  tail  be  formed  by  an  outpouring  of  matter  from 
the  comet,  which  only  takes  place  when  the  comet  is  near 
the  sun,  the  more  often  a  comet  approaches  the  sun  the 
more  must  it  waste  away  ;  and  we  find  accordingly  that  the 
short-period  comets,  which  return  to  the  neighbourhood  of 
the  sun  at  frequent  intervals  (§  291),  are  inconspicuous 
bodies.  The  same  theory  is  supported  by  the  shape  of  the 
tail.  In  some  cases  it  is  straight,  but  more  commonly  it  is 
curved  to  some  extent,  and  the  curvature  is  then  always 
backwards  in  relation  to  the  comet's  motion.  Now  by 
ordinary  dynamical  principles  matter  shot  off  from  the  head 
of  the  comet  while  it  is  revolving  round  the  sun  would 
tend,  as  it  were,  to  lag  behind  more  and  more  the  farther 
it  receded  from  the  head,  and  an  apparent  backward 
curvature  of  the  tail — less  or  greater  according  to  the  speed 
with  which  the  particles  forming  the  tail  were  repelled — 
would  be  the  result.  Variations  in  curvature  of  the  tails 
of  different  comets,  and  the  existence  of  two  or  more 
differently  curved  tails  of  the  same  comet,  are  thus  readily 
explained  by  supposing  them  made  of  different  materials, 
repelled  from  the  comet's  head  at  different  speeds. 

The  first  application  of  the  spectroscope  to  the  study  of 
comets  was  made  in  1864  by  Giambattista  Donati  (1826- 
1873),  best  known  as  the  discoverer  of  the  magnificent 
comet  of  1858.  A  spectrum  of  three  bright  bands,  wider 
than  the  ordinary  "  lines,"  was  obtained,  but  they  were 
not  then  identified.  Four  years  later  Sir  William  Huggins 
obtained  a  similar  spectrum,  and  identified  it  with  that 
of  a  compound  of  carbon  and  hydrogen.  Nearly  every 
comet  examined  since  then  has  shewn  in  its  spectrum 
bright  bands  indicating  the  presence  of  the  same  or  some 
other  hydrocarbon,  but  in  a  few  cases  other  substances 
have  also  been  detected.  A  comet  is  therefore  in  part 
at  least  self-luminous,  and  some  of  the  light  which  it  sends 
us  is  that  of  a  glowing  gas.  It  also  shines  to  a  considerable 
extent  by  reflected  sunlight ;  there  is  nearly  always  a  con- 


$  305]  Comets  and  Meteors  395 

tinuous  spectrum,  and  in  a  few  cases— first  in  1881 — the 
spectrum  has  been  distinct  enough  to  shew  the  Fraunhofer 
lines  crossing  it.  But  the  continuous  spectrum  seems  also 
to  be  due  in  part  to  solid  or  liquid  matter  in  the  comet  itself, 
which  is  hot  enough  to  be  self-luminous. 

305.  The  work  of  the  last  30  or  40  years  has  established 
a  remarkable  relation  between  comets  and  the  minute  bodies 
which  are  seen  in  the  form  of  meteors  or  shooting  stars. 
Only  a  few  of  the  more  important  links  in  the  chain  of 
evidence  can,  however,  be  mentioned.  Showers  of  shooting 
stars,  the  occurrence  of  which  has  been  known  from  quite 
early  times,  have  been  shewn  to  be  due  to  the  passage  of 
the  earth  through  a  swarm  of  bodies  revolving  in  elliptic 
orbits  round  the  sun.  The  paths  of  four  such  swarms 
were  ascertained  with  some  precision  in  1866-67,  and  found 
in  each  case  to  agree  closely  with  the  paths  of  known 
comets.  And  since  then  a  considerable  number  of  other 
cases  of  resemblance  or  identity  between  the  paths  of 
meteor  swarms  and  of  comets  have  been  detected.  One 
of  the  four  comets  just  referred  to,  known  as  Biela's,  with 
a  period  of  between  six  and  seven  years,  was  duly  seen  on 
several  successive  returns,  but  in  1845-46  was  observed 
first  to  become  somewhat  distorted  in  shape,  and  afterwards 
to  have  divided  into  two  distinct  comets  ;  at  the  next  return 
(1852)  the  pair  were  again  seen;  but  since  then  nothing 
has  been  seen  of  either  portion.  At  the  end  of  November  in 
each  year  the  earth  almost  crosses  the  path  of  this  comet,  and 
on  two  occasions  (1872,  and  1885)  it  did  so  nearly  at  the  time 
when  the  comet  was  due  at  the  same  spot ;  if,  as  seemed 
likely,  the  comet  had  gone  to  pieces  since  its  last  appearance, 
there  seemed  a  good  chance  of  falling  in  with  some  of  its 
remains,  and  this  expectation  was  fulfilled  by  the  occurrence 
on  both  occasions  of  a  meteor  shower  much  more  brilliant 
than  that  usually  observed  at  the  same  date. 

Biela's  comet  is  not  the  only  comet  which  has  shewn 
signs  of  breaking  up;  Brooks's  comet  of  1889,  which  is 
probably  identical  with  Lexell's  (chapter  XL,  §  248),  was 
found  to  be  accompanied  by  three  smaller  companions ; 
as  this  comet  has  more  than  once  passed  extremely  close 
to  Jupiter,  a  plausible  explanation  of  its  breaking  up  is  at 
once  given  in  the  attractive  force  of  the  planet.  Moreover 


396  A  Short  History  of  Astronomy          [CH.  XHI. 

certain  systems  of  comets,  the  members  of  which  revolve 
in  the  same  orbit  but  separated  by  considerable  intervals 
of  time,  have  also  been  discovered.  Tebbutt's  comet  of 
1 88 1  moves  in  practically  the  same  path  as  one  seen  in 
1807,  and  the  great  comet  of  1880,  the  great  comet  of  1882 
(shewn  in  fig.  99),  and  a  third  which  appeared  in  1887, 
all  move  in  paths  closely  resembling  that  of  the  comet  of 
1843,  while  that  of  1668  is  more  doubtfully  connected 
with  the  same  system.  And  it  is  difficult  to  avoid  regarding 
the  members  of  a  system  as  fragments  of  an  earlier  comet, 
which  has  passed  through  the  stages  in  which  we  have 
actually  seen  the  comets  of  Biela  and  Brooks. 

Evidence  of  such  different  kinds  points  to  an  intimate 
connection  between  comets  and  meteors,  though  it  is 
perhaps  still  premature  to  state  confidently  that  meteors 
are  fragments  of  decayed  comets,  or  that  conversely  comets 
are  swarms  of  meteors. 

306.  Each  of  the  great  problems  of  sidereal  astronomy 
which  Herschel  formulated  and  attempted  to  solve  has 
been  elaborately  studied  by  the  astronomers  of  the  i9th 
century.  The  multiplication  of  observatories,  improve- 
ments in  telescopes,  and  the  introduction  of  photography — to 
mention  only  three  obvious  factors  of  progress — have  added 
enormously  to  the  extent  and  accuracy  of  our  knowledge  of 
the  stars,  while  the  invention  of  spectrum  analysis  has  thrown 
an  entirely  new  light  on  several  important  problems. 

William  Herschel's  most  direct  successor  was  his  son 
John  Frederick  William  (1792-1871),  who  was  not  only  an 
astronomer,  but  also  made  contributions  of  importance  to 
pure  mathematics,  to  physics,  to  the  nascent  art  of  photo- 
graphy, and  to  the  philosophy  of  scientific  discovery.  He 
began  his  astronomical  career  about  1816  by  re-measuring, 
first  alone,  then  in  conjunction  with  fames  South  (1785- 
1867),  a  number  of  his  father's  double  stars.  The  first 
result  of  this  work  was  a  catalogue,  with  detailed  measure- 
ments, of  some  hundred  double  and  multiple  stars  (published 
in  1824),  which  formed  a  valuable  third  term  of  comparison 
with  his  father's  observations  of  1781-82  and  1802-03,  and 
confirmed  in  several  cases  the  slow  motions  of  revolution 
the  beginnings  of  which  had  been  observed  before.  A 
great  survey  of  nebulae  followed,  resulting  in  a  catalogue 


$$  306,  307  Tohn  Herschel  397 

(1833)  of  about  2500,  of  which  some  500  were  new  and 
2000  were  his  father's,  a  few  being  due  to  other  observers  ; 
incidentally  more  than  3000  pairs  of  stars  close  enough 
together  to  be  worth  recording  as  double  stars  were  observed. 

307.  Then  followed  his  well-known  expedition  to  the 
Cape  of  Good  Hope  (1833-1838),  where  he  "swept"  the 
southern  skies  in  very  much  the  same  way  in  which  his 
father  had  explored  the  regions  visible  in  our  latitude. 
Some  1200  double  and  multiple  stars,  and  a  rather  larger 
number  of  new  nebulae,  were  discovered  and  studied,  while 
about  500  known  nebulae  were  re-observed ;  star-gauging  on 
William  Herschel's  lines  was  also  carried  out  on  an  extensive 
scale.  A  number  of  special  observations  of  interest  were 
made  almost  incidentally  during  this  survey  :  the  remarkable 
variable  star  17  Argus  and  the  nebula  surrounding  it  (a 
modern  photograph  of  which  is  reproduced  in  fig.  100),  the 
wonderful  collections  of  nebulae  clusters  and  stars,  known 
as  the  Nubeculae  or  Magellanic  Clouds,  and  Halley's  comet 
were  studied  in  turn;  and  the  two  faintest  satellites  of 
Saturn  then  known  (chapter  xn.,  §  255)  were  seen  again 
for  the  first  time  since  the  death  of  their  discoverer. 

An  important  investigation  of  a  somewhat  different 
character — that  of  the  amount  of  heat  received  from  the 
sun — was  also  carried  out  (1837)  during  Herschel's  residence 
at  the  Cape  ;  and  the  result  agreed  satisfactorily  with  that 
of  an  independent  inquiry  made  at  the  same  time  in  France 
by  Claude  Servais  Mathias  Pouillet  (1791-1868).  In  both 
cases  the  heat  received  on  a  given  area  of  the  earth  in  a 
given  time  from  direct  sunshine  was  measured ;  and  allow- 
ance being  made  for  the  heat  stopped  in  the  atmosphere 
as  the  sun's  rays  passed  through  it,  an  estimate  was  formed 
of  the  total  amount  of  heat  received  annually  by  the  earth 
from  the  sun,  and  hence  of  the  total  amount  radiated  by 
the  sun  in  all  directions,  an  insignificant  fraction  of  which 
(one  part  in  2,000,000,000)  is  alone  intercepted  by  the 
earth.  But  the  allowance  for  the  heat  intercepted  in  our 
atmosphere  was  necessarily  uncertain,  and  later  work,  in 
particular  that  of  Dr.  S.  P.  Langley  in  1 880-81,  shews  that 
it  was  very  much  under-estimated  by  both  Herschel  and 
Pouillet.  According  to  Herschel's  results,  the  heat  received 
annually  from  the  sun — including  that  intercepted  in  the 


398  A  Short  History  of  Astronomy          [CH.  xill. 

atmosphere — would  be  sufficient  to  melt  a  shell  of  ice 
120  feet  thick  covering  the  whole  earth;  according  to 
Dr.  Langley,  the  thickness  would  be  about  160  feet.* 

308.  With   his   return   to   England   in    1838   Herschel's 
career  as  an  observer  came  to  an  end  ;  but  the  working  out 
of  the  results  of  his  Cape   observations,    the   arrangement 
and   cataloguing   of  his   own  and   his  father's  discoveries, 
provided  occupation  for  many  years.     A  magnificent  volume 
on  the  Results  of  Astronomical  Observations  made  during  the 
years  1834-8  at  the  Cape  of  Good  Hope  appeared  in  1847  ; 
and  a  catalogue  o£  all  known  nebulae  and  clusters,  amount- 
ing to  5,079,  was  presented  to  the  Royal  Society  in  1864, 
while  a  corresponding  catalogue  of  more  than  10,000  double 
and  multiple  stars  was  never  finished,  though  the  materials 
collected  for  it  were  published  posthumously  in  1879.     Jonn 
Herschel's  great  catalogue  of  nebulae  has  since  been  revised 
and  enlarged  by  Dr.  Dreyer,  the  result  being  a  list  of  7,840 
nebulae  and  clusters   known  up  to  the  end  of  1887  ;  and 
a    supplementary    list    of    discoveries    made    in    1888-94 
published  by  the  same  writer  contains  1,529  entries,  so  that 
the  total  number  now  known  is  between  9,000  and  io,oco, 
of  which  more  than  half  have  been  discovered  by  the  two 
Herschels. 

309.  Double  stars  have  been  discovered  and  studied  by 
a  number  of  astronomers  besides  the  Herschels.     One  of 
the  most  indefatigable  workers  at  this  subject  was  the  elder 
Struve  (§  279),  who  was  successively  director  of  the   two 
Russian    observatories     of    Dorpat    and    Pulkowa.      He 
observed  altogether  some  2,640  double  and  multiple  stars, 
measuring  in  each  case  with  care  the  length  and  direction 
of  the  line  joining  the  two  components,  and  noting  other 
peculiarities,    such    as  contrasts    in    colour    between    the 
members  of  a  pair.     He  paid  attention  only  to  double  stars 
the  two  components  of  which  were  not  more  than  32''  apart, 
thus  rejecting  a  good  many  which  William  Herschel  would 
have  noticed ;  as  the   number  of  known   doubles   rapidly 
increased,  it  was  clearly  necessary  to  concentrate  attention 
on   those   which   might  with   some   reasonable   degree   of 

*  Observations  made  on  Mont  Blanc  under  the  direction  of 
M.  Janssen  in  1897  indicate  a  slightly  larger  number  than  Dr. 
Langley 's. 


3°8,  309] 


Double  Stars 


399 


probability  turn  out  to  be  genuine   binaries  (chapter  xii., 
§  264). 

In  addition  to  a  number  of  minor  papers  Struve  published 
three  separate  books  on  the  subject  in  1827,  1837,  and  1852.* 
A  comparison  of  his  own  earlier  and  later  observations,  and 
of  both  with  Herschel's  earlier  ones,  shewed  about  TOO  cases 
of  change  of  relative  positions  of  two  members  of  a  pair, 
which  indicated  more  or  less  clearly  a  motion  of  revolution, 
and  further  results  of  a  like  character  have  been  obtained 


Scale. 


880 


FIG.  101. — The  orbit  of  £  Ursae,  shewing  the  relative  positions  of 
the  two  components  at  various  times  between  1781  and  1897. 
(The  observations  of  1781  and  1802  were  only  enough  to 
determine  the  direction  of  the  line  joining  the  two  components, 
not  its  length.) 

from  a  comparison  of  Struve's  observations  with  those  of 
later  observers. 

William  Herschel's  observations  of  binary  systems 
(chapter  xii.,  §  264)  only  sufficed  to  shew  that  a  motion  of 
revolution  of  some  kind  appeared  to  be  taking  place ;  it 
was  an  obvious  conjecture  that  the  two  members  of  a  pair 

*  Catalogus  novus  stettarunt  duplicium,  Stellarutn  duplicium  et 
multiplicium  mensurac  micromelricae,  and  Stcllantm  fixarum  imprimis 
duplicium  et  multiplicium  positiones  mediae  pro  epocha  1830. 


400  A  Short  History  of  Astronomy          [Cn.  xni. 

attracted  one  another  according  to  the  law  of  gravitation, 
so  that  the  motion  of  revolution  was  to  some  extent 
analogous  to  that  of  a  planet  round  the  sun ;  if  this  were 
the  case,  then  each  star  of  a  pair  should  describe  an  ellipse 
(or  conceivably  some  other  conic)  round  the  other,  or  each 
round  the  common  centre  of  gravity,  in  accordance  with 
Kepler's  laws,  and  the  apparent  path  as  seen  on  the  sky 
should  be  of  this  nature  but  in  general  foreshortened  by 
being  projected  on  to  the  celestial  sphere.  The  first  attempt 
to  shew  that  this  was  actually  the  case  was  made  by  Felix 
Savary  (1797-1841)  in  1827,  the  star  being  £  Ursae,  which 
was  found  to  be  revolving  in  a  period  of  about  60  years. 

Many  thousand  double  stars  have  been  discovered  by 
the  Herschels,  Struve,  and  a  number  of  other  observers, 
including  several  living  astronomers,  among  whom  Pro- 
fessor S.  W.  Burnham  of  Chicago,  who  has  discovered 
some  1300,  holds  a  leading  place.  Among  these  stars  there 
are  about  300  which  we  have  fair  reason  to  regard  as 
binary,  but  not  more  than  40  or  50  of  the  orbits  can  be 
regarded  as  at  all  satisfactorily  known.  One  of  the  most 
satisfactory  is  that  of  Savary's  star  £  Ursae,  which  is  shewn 
in  fig.  i oi.  Apart  from  the  binaries  discovered  by  the 
spectroscopic  method  (§  314),  which  form  to  some  extent 
a  distinct  class,  the  periods  of  revolution  which  have  been 
computed  range  between  about  ten  years  and  several 
centuries,  the  longer  periods  being  for  the  most  part 
decidedly  uncertain. 

310.  William  Herschel's  telescopes  represented  for  some 
time  the  utmost  that  could  be  done  in  the  construction  of 
reflectors ;  the  first  advance  was  made  by  Lord  Rosse 
(1800-1867),  who— after  a  number  of  less  successful  ex- 
periments— finally  constructed  (1845),  at  Parsonstown  in 
Ireland,  a  reflecting  telescope  nearly  60  feet  in  length,  with 
a  mirror  which  was  six  feet  across,  and  had  consequently  a 
"  light-grasp  "  more  than  double  that  of  Herschel's  greatest 
telescope.  Lord  Rosse  used  the  new  instrument  in  the  first 
instance  to  re-examine  a  number  of  known  nebulae,  and  in 
the  course  of  the  next  few  years  discovered  a  variety  of  new 
features,  notably  the  spiral  form  of  certain  nebulae  (fig.  102), 
and  the  resolution  into  apparent  star  clusters  of  a  number 
of  nebulae  which  Herschel  had  been  unable  to  resolve 


Iff 


FIG.   102. — Spiral  nebulae.      From  drawings  by  Lord  Rosse. 

\Tofacep  400. 


§§  310—312]  Double  Stars  and  Nebulae  401 

and  had  accordingly  put  into  "  the  shining  fluid "  class 
(chapter  xii.,  §  260).  This  last  discovery,  being  exactly 
analogous  to  Herschel's  experience  when  he  first  began  to 
examine  nebulae  hitherto  only  observed  with  inferior  tele- 
scopes, naturally  led  to  a  revival  of  the  view  that  nebulae 
are  indistinguishable  from  clusters  of  stars,  though  many 
of  the  arguments  from  probability  urged  by  Herschel  and 
others  were  in  reality  unaffected  by  the  new  discoveries. 

311.  The  question  of  the  status  of  nebulae  in  its  simplest 
form    may    be    said   to    have    been    settled    by  the    first 
application  of  spectrum  analysis.     Fraunhofer  (§  299)  had 
seen  as  early  as  1823  that  stars  had  spectra  characterised 
like   that   of  the  sun  by  dark  lines,  and   more   complete 
investigations  made  soon  after  Kirchhoff's  discoveries  by 
several  astronomers,  in  particular  by  Sir  William  Huggins 
and    by    the    eminent    Jesuit    astronomer    Angela    Secchi 
(1818-1878),  confirmed   this  result  as   regards   nearly   all 
stars  observed. 

The  first  spectrum  of  a  nebula  was  obtained  by  Sir 
William  Huggins  in  1864,  and  was  seen  to  consist  of  three 
bright  lines;  by  1868  he  had  examined  70,  and  found  in 
about  one-third  of  the  cases,  including  that  of  the  Orion 
nebula,  a  similar  spectrum  of  bright  lines.  In  these  cases 
therefore  the  luminous  part  of  the  nebula  is  gaseous,  and 
Herschel's  suggestion  of  a  "  shining  fluid  "  was  confirmed 
in  the  most  satisfactory  way.  In  nearly  all  cases  three 
bright  lines  are  seen,  one  of  which  is  a  hydrogen  line,  while 
the  other  two  have  not  been  identified,  and  in  the  case  of 
a  few  of  the  brighter  nebulae  some  other  lines  have  also 
been  seen.  On  the  other  hand,  a  considerable  number  of 
nebulae,  including  many  of  those  which  appear  capable  of 
telescopic  resolution  into  star  clusters,  give  a  continuous 
spectrum,  so  that  there  is  no  clear  spectroscopic  evidence 
to  distinguish  them  from  clusters  of  stars,  since  the  dark 
lines  seen  usually  in  the  spectra  of  the  latter  could  hardly 
be  expected  to  be  visible  in  the  case  of  such  faint  objects 
as  nebulae. 

312.  Stars  have  been  classified,  first  by  Secchi  (1863), 
afterwards  in  slightly  different  ways  by  others,  according  to 
the  general  arrangement  of  the  dark  lines  in  their  spectra ; 
and  some  attempts   have  been   made  to  base   on   these 

26 


402  A  Short  History  of  Astronomy          [Cn.  xin. 

differences  inferences  as  to  the  relative  "  ages,"  or  at  any 
rate  the  stages  of  development,  of  different  stars. 

Many  of  the  dark  lines  in  the  spectra  of  stars  have  been 
identified,  first  by  Sir  William  Huggins  in  1864,  with  the 
lines  of  known  terrestrial  elements,  such  as  hydrogen,  iron, 
sodium,  calcium  ;  so  that  a  certain  identity  between  the 
materials  of  which  our  own  earth  is  made  and  that  of 
bodies  so  remote  as  the  fixed  stars  is  thus  established. 

In  addition  to  the  classes  of  stars  already  mentioned,  the 
spectroscope  has  shewn  the  existence  of  an  extremely  in- 
teresting if  rather  perplexing  class  of  stars,  falling  into 
several  subdivisions,  which  seem  to  form  a  connecting 
link  between  ordinary  stars  and  nebulae,  for,  though  in- 
distinguishable telescopically  from  ordinary  stars,  their 
spectra  shew  bright  lines  either  periodically  or  regularly. 
A  good  many  stars  of  this  class  are  variable,  and  several 
"  new  "  stars  which  have  appeared  and  faded  away  of  late 
years  have  shewn  similar  characteristics. 

313.  The  first  application  to  the  fixed  stars  of  the  spectro- 
scopic  method  (§  302)  of  determining  motion  towards  or  away 
from  the  observer  was  made  by  Sir  William  Huggins  in  1868. 
A  minute  displacement  from  its  usual  position  of  a  dark 
hydrogen  line  (F)  in  the  spectrum  of  Sirius  was  detected, 
and  interpreted  as  shewing  that  the  star  was  receding  from 
the  solar  system  at  a  considerable  speed.     A  number  of 
other  stars  were  similarly  observed  in  the  following  year, 
and  the  work  has  been  taken  up  since   by  a  number  of 
other  observers,   notably  at  Potsdam  under  the   direction 
of  Professor  H.  C.   Vogel,  and  at  Greenwich. 

314.  A  very  remarkable  application  of  this  method  to 
binary   stars   has   recently   been  made.     If  two   stars  are 
revolving  round  one   another,  their  motions   towards   and 
away  from  the  earth  are  changing  regularly  and  are  differ- 
ent ;  hence,  if  the  light  from  both  stars  is  received  in  the 
spectroscope,  two  spectra  are  formed — one  for  each  star — 
the  lines  of  which  shift  regularly  relatively  to  one  another. 
If  a  particular  line,  say  the  F  line,  common  to  the  spectra 
of  both   stars,   is  observed  when   both   stars  are  moving 
towards  (or  away  from)  the  earth  at  the  same  rate — which 
happens  twice  in  each  revolution — only  one  line  is  seen ; 
but  when  they  are  moving  differently,  if  the  spectroscope 


*§  313-316]  Stellar  Spectroscopy  403 

be  powerful  enough  to  detect  the  minute  quantity  involved, 
the  line  will  appear  doubled,  one  component  being  due  to 
one  star  and  one  to  the  other.  A  periodic  doubling  of 
this  kind  was  detected  at  the  end  of  1889  by  Professor 
E.  C.  Pickering  of  Harvard  in  the  case  of  £  Ursae,  which 
was  thus  for  the  first  time  shewn  to  be  binary,  and  found 
to  have  the  remarkably  short  period  of  only  104  days. 
This  discovery  was  followed  almost  immediately  by  Pro- 
fessor Vogel's  detection  of  a  periodical  shift  in  the  position 
of  the  dark  lines  in  the  spectrum  of  the  variable  star  Algol 
(chapter  xn.,  §  266) ;  but  as  in  this  case  no  doubling  of  the 
lines  can  be  seen,  the  inference  is  that  the  companion  star 
is  nearly  or  quite  dark,  so  that  as  the  two  revolve  round 
one  another  the  spectrum  of  the  bright  star  shifts  in  the 
manner  observed.  Thus  the  eclipse-theory  of  Algol's 
variability  received  a  striking  verification. 

A  number  of  other  cases  of  both  classes  of  spectroscopic 
binary  stars  (as  they  may  conveniently  be  called)  have 
since  been  discovered.  The  upper  part  of  fig.  103  shews 
the  doubling  of  one  of  the  lines  in  the  spectrum  of  the 
double  star  ft  Aurigae ;  and  the  lower  part  shews  the 
corresponding  part  of  the  spectrum  at  a  time  when  the  line 
appeared  single. 

315.  Variable  stars  of  different   kinds  have   received  a 
good   deal   of  attention   during   this    century,   particularly 
during  the  last  few  years.     About  400  stars  are  now  clearly 
recognised  as  variable,  while  in  a  large  number  of  other 
cases  variability  of  light  has  been  suspected ;  except,  how- 
ever,  in  a  few  cases,   like  that  of  Algol,  the   causes  of 
variability  are  still  extremely  obscure. 

316.  The   study   of  the  relative  brightness  of  stars — a 
branch  of  astronomy  now  generally  known  as  stellar  photo- 
metry— has  also  been  carried   on   extensively  during   the 
century  and  has  now  been  put  on  a  scientific  basis.     The 
traditional  classification  of  stars  into  magnitudes,  according 
to   their    brightness,    was    almost    wholly    arbitrary,    and 
decidedly  uncertain.     As   soon  as  exact  quantitative  com- 
parisons of  stars  of  different  brightness  began  to  be  carried 
out  on  a  considerable  scale,  the  need  of  a  more  precise 
system  of  classification  became  felt.     John  Herschel  was 
one  of  the  pioneers  in  this  direction ;  he  suggested  a  scale 


404  A  Short  History  of  Astronomy          [CH.  xm. 

capable  of  precise  expression,  and  agreeing  roughly,  at 
any  rate  as  far  as  naked-eye  stars  are  concerned,  with  the 
current  usages ;  while  at  the  Cape  he  measured  carefully 
the  light  of  a  large  number  of  bright  stars  and  classified 
them  on  this  principle.  According  to  the  scale  now  gener- 
ally adopted,  first  suggested  in  1856  by  Norman  Robert 
Pogson  (1829-1891),  the  lig'it  of  a  star  of  any  magnitude 
bears  a  fixed  ratio  (which  is  taken  to  be  2 '5 12...)  to  that 
of  a  star  of  the  next  magnitude.  The  number  is  so  chosen 
that  a  star  of  the  sixth  magnitude — thus  defined — is  100 
times  fainter  than  one  of  the  first  magnitude.*  Stars  of 
intermediate  brightness  have  magnitudes  expressed  by 
fractions  which  can  be  at  once  calculated  (according  to 
a  simple  mathematical  rule)  when  the  ratio  of  the  light 
received  from  the  star  to  that  received  from  a  standard  star 
has  been  observed. t 

Most  of  the  great  star  catalogues  (§  280)  have  included 
estimates  of  the  magnitudes  of  stars.  The  most  extensive 
and  accurate  series  of  measurements  of  star  brightness  have 
been  those  executed  at  Harvard  and  at  Oxford  under  the 
superintendence  of  Professor  E.  C.  Pickering  and  the  late 
Professor  Pritchard  respectively.  Both  catalogues  deal  with 
stars  visible  to  the  naked  eye ;  the  Harvard  catalogue 
(published  in  1884)  comprises  4,260  stars  between  the 
North  Pole  and  30°  southern  declination,  and  the  Urano- 
metria  Nova  Oxoniensis  (1885),  as  it  is  called,  only  goes 
10°  south  of  the  equator  and  includes  2,784  stars.  Portions 
of  more  extensive  catalogues  dealing  with  fainter  stars,  in 
progress  at  Harvard  and  at  Potsdam,  have  also  been 
published. 

*  I.e.  2-512...  is  chosen  as  being  the  number  the  logarithm  of  which 
is  -4,  so  that  (2-5 12... )5'2  =  10. 

•f  If  L  be  the  ratio  of  the  light  received  from  a  star  to  that  received 
from  a  standard  first  magnitude  star,  such  as  Aldebaran  or  Altair, 
then  its  magnitude  m  is  given  by  the  formula 

m  -  1 

m  - 1       /    I    \     5           ,                                    SIT 
=  I 1          ,  whence  m  —  I  = log  L. 


5'5I2/  \IOO/  2 

A  star  brighter  than  Aldebaran  has  a  magnitude  less  than  I,  while 
the  magnitude  of  Sirius,  which  is  about  nine  times  as  bright  as 
Aldebaran,  is  a  negative  quantity,  —  1-4,  according  to  the  Harvard 
photometry. 


FIG.   104. — The  Milky  Way  near  the  cluster  in  Perseus, 
by  Professor  Barnard. 


From  a  photograph 
[To  face  P-  4°5- 


$  si?]  Photometry :  the  Sidereal  System  405 

317.  The  great  problem  to  which  Herschel  gave  so 
much  attention,  that  of  the  general  arrangement  of  the 
stars  and  the  structure  of  the  system,  if  any,  formed 
by  them  and  the  nebulae,  has  been  affected  in  a  variety 
of  ways  by  the  additions  which  have  been  made  to  our 
knowledge  of  the  stars.  But  so  far  are  we  from  any 
satisfactory  solution  of  the  problem  that  no  modern  theory 
cm  fairly  claim  to  represent  the  facts  now  known  to  us  as  we! I 
as  Herschel's  earlier  theory  fitted  the  much  scantier  stock 
which  he  had  at  his  command.  In  this  as  in  so  many 
cases  an  increase  of  knowledge  has  shewn  the  insufficiency 
of  a  previously  accepted  theory,  but  has  not  provided  a 
successor.  Detailed  study  of  the  form  of  the  Milky  Way 
(cf.  fig.  104)  and  of  its  relation  to  the  general  body  of  stars 
has  shewn  the  inadequacy  of  any  simple  arrangement  of 
stars  to  represent  its  appearance  ;  William  Herschel's  cloven 
grindstone,  the  ring  which  his  son  was  inclined  to  substitute 
for  it  as  the  result  of  his  Cape  studies,  and  the  more 
complicated  forms  which  later  writers  have  suggested,  alike 
fail  to  account  for  its  peculiarities.  Again,  such  evidence 
as  we  have  of  the  distance  of  the  stars,  when  compared 
with  their  brightness,  shews  that  there  are  large  variations 
in  their  actual  sizes  as  well  as  in  their  apparent  sizes,  and 
thus  tells  against  the  assumption  of  a  certain  uniformity 
which  underlay  much  of  Herschel's  work.  The  "  island 
universe "  theory  of  nebulae,  partially  abandoned  by 
Herschel  after  1791  (chapter  xn.,  §  260),  but  brought  into 
credit  again  by  Lord  Rosse's  discoveries  (§  310),  scarcely 
survived  the  spectroscopic  proof  of  the  gaseous  character 
of  certain  nebulae.  Other  evidence  has  pointed  clearly  to 
intimate  relations  between  nebulae  and  stars  generally ; 
Herschel's  observation  that  nebulae  are  densest  in  regions 
farthest  from  the  Milky  Way  has  been  abundantly  verified 
— as  far  as  irresoluble  nebulae  are  concerned — while 
obvious  star  clusters  shew  an  equally  clear  preference  for 
the  neighbourhood  of  the  Milky  Way.  In  many  cases  again 
individual  stars  or  groups  seen  on  the  sky  in  or  near  a 
nebula  have  been  clearly  shewn,  either  by  their  arrangement 
or  in  some  cases  by  peculiarities  of  their  spectra,  to  be  really 
connected  with  the  nebula,  and  not  merely  to  be  accident- 
ally in  the  same  direction.  Stars  which  have  bright  lines 


406  A  Short  History  of  Astronomy          [CH.  xin. 

in    their    spectra    (§  312)    form    another    link    connecting 
nebulae  with  stars. 

A  good  many  converging  lines  of  evidence  thus  point 
to  a  greater  variety  in  the  arrangement,  size,  and  structure 
of  the  bodies  with  which  the  telescope  makes  us  acquainted 
than  seemed  probable  when  sidereal  astronomy  was  first 
seriously  studied ;  they  also  indicate  the  probability  that 
these  bodies  should  be  regarded  as  belonging  to  a 
single  system,  even  if  it  be  of  almost  inconceivable 
complexity,  rather  than  to  a  number  of  perfectly  distinct 
systems  of  a  simpler  type. 

318.  Laplace's  nebular  hypothesis  (chapter  XL,   §   250) 
was  published  a  little  more  than  a  century  ago  (1796),  and 
has  been  greatly  affected   by  progress   in  various  depart- 
ments of  astronomical  knowledge.     Subsequent  discoveries 
of  planets  and  satellites  (§§  294,  295)  have  marred  to  some 
extent  the  uniformity  and  symmetry  of  the  motions  of  the 
solar  system  on  which  Laplace  laid  so  much  stress  ;  but  it 
is  not  impossible   to  give   reasonable   explanations  of  the 
backward  motions  of  the  satellites  of  the  two  most  distant 
planets,  and  o'f  the  large  eccentricity  and  inclination  of  the 
paths  of  some  of  the  minor  planets,  while  apart  from  these 
exceptions   the   number  of  bodies   the   motions  of  which 
have   the   characteristics   which    Laplace   pointed   out  has 
been  considerably  increased.     The  case  for  some  sort  of 
common  origin  of  the  bodies  of  the  solar  system  has  per- 
haps in  this  way  gained  as  much  as  it  has  lost.     Again,  the 
telescopic  evidence  which  Herschel  adduced  (chapter  xn., 
§  261)  in  favour  of  the  existence  of  certain   processes  of 
condensation  in  nebulae  has  been   strengthened   by  later 
evidence  of  a  similar  character,  and  by  the  various  pieces 
of  evidence  already  referred  to  which  connect  nebulae  with 
single  stars  and   with  clusters.     The   differences    in    the 
spectra  of  stars  also  receive  their  most  satisfactory  explana- 
tion  as   representing   different   stages   of  condensation   of 
bodies  of  the  same  general  character. 

319.  An   entirely  new  contribution   to  the  problem  has 
resulted  from  certain  discoveries  as  to  the  nature  of  heat, 
culminating  in  the  recognition  (about  1840-50)  of  heat  as 
only  one  form  of  what  physicists  no\»  call  energy,  which 
manifests   itself   also    in    the    motion   of    bodies,   in   the 


**  3»8,  319]      The  Evolution  of  the  Solar  System  407 

separation  of  bodies  which  attract  one  another,  as  well  as 
in  various  electrical,  chemical,  and  other  ways.  With  this 
discovery  was  closely  connected  the  general  theory  known 
as  the  conservation  of  energy,  according  to  which  energy, 
though  capable  of  many  transformations,  can  neither  be 
increased  nor  decreased  in  quantity.  A  body  which,  like 
the  sun,  is  giving  out  heat  and  light  is  accordingly  thereby 
losing  energy,  and  is  like  a  machine  doing  work ;  either 
then  it  is  receiving  energy  from  some  other  source  to 
compensate  this  loss  or  its  store  of  energy  is  diminishing. 
But  a  body  which  goes  on  indefinitely  giving  out  heat  and 
light  without  having  its  store  of  energy  replenished  is 
exactly  analogous  to  a  machine  which  goes  on  working 
indefinitely  without  any  motive  power  to  drive  it ;  and  both 
are  alike  impossible. 

The  results  obtained  by  John  Herschel  and  Pouillet  in 
^36  (§  307)  called  attention  to  the  enormous  expenditure 
of  the  sun  in  the  form  of  heat,  and  astronomers  thus  had  to 
face  the  problem  of  explaining  how  the  sun  was  able  to  go 
on  radiating  heat  and  light  in  this  way.  Neither  in  the 
few  thousand  years  of  the  past  covered  by  historic  records, 
nor  in  the  enormously  great  periods  of  which  geologists 
and  biologists  take  account,  is  there  any  evidence  of  any 
important  permanent  alteration  in  the  amount  of  heat  and 
light  received  annually  by  the  earth  from  the  sun.  Any 
theory  of  the  sun's  heat  must  therefore  be  able  to  account 
for  the  continual  expenditure  of  heat  at  something  like  the 
present  rate  for  an  immense  period  of  time.  The  obvious 
explanation  of  the  sun  as  a  furnace  deriving  its  heat  from 
combustion  is  found  to  be  totally  inadequate  when  put  to 
the  test  of  figures,  as  the  sun  could  in  this  way  be  kept 
going  at  most  for  a  few  thousand  years.  The  explanation 
now  generally  accepted  was  first  given  by  the  great  German 
physicist  Hermann  von  Helmholtz  (1821-1894)  in  a  popular 
lecture  in  1854.  The  sun  possesses  an  immense  store  of 
energy  in  the  form  of  the  mutual  gravitation  of  its  parts  ; 
if  from  any  cause  it  shrinks,  a  certain  amount  of  gravita- 
tional energy  is  necessarily  lost  and  takes  some  other  form. 
In  the  shrinkage  of  the  sun  we  have  therefore  a  possible 
source  of  energy.  The  precise  amount  of  energy  liberated 
by  a  definite  amount  of  shrinkage  of  the  sun  depends  upon 


408  A  Short  History  of  Astronomy          [CH.  xui. 

the  internal  distribution  of  density  in  the  sun,  which  is 
uncertain,  but  making  any  reasonable  assumption  as  to  this 
we  find  that  the  amount,  of  shrinking  required  to  supply 
the  sun's  expenditure  of  heat  would  only  diminish  the 
diameter  by  a  few  hundred  feet  annually,  and  would 
therefore  be  imperceptible  with  our  present  telescopic 
power  for  centuries,  while  no  earlier  records  of  the  sun's 
size  are  accurate  enough  to  shew  it.  It  is  easy  to  calculate 
on  the  same  principles  the  amount  of  energy  liberated  by  a 
body  like  the  sun  in  shrinking  from  an  indefinitely  diffused 
condition  to  its  present  state,  and  from  its  present  state  to 
one  of  assigned  greater  density;  the  result  being  that  we 
can  in  this  way  account  for  an  expenditure  of  sun-heat  at 
the  present  rate  for  a  period  to  be  counted  in  millions  of 
years  in  either  past  or  future  time,  while  if  the  rate  of 
expenditure  was  less  in  the  remote  past  or  becomes  less 
in  the  future  the  time  is  extended  to  a  corresponding 
extent. 

No  other  cause  that  has  been  suggested  is  competent 
to  account  for  more  than  a  small  fraction  of  the  actual 
heat-expenditure  of  the  sun ;  the  gravitational  theory 
satisfies  all  the  requirements  of  astronomy  proper,  and  goes 
at  any  rate  some  way  towards  meeting  the  demands  of 
biology  and  geology. 

If  then  we  accept  it  as  provisionally  established,  we 
are  led  to  the  conclusion  that  the  sun  was  in  the  past 
larger  and  less  condensed  than  now,  and  by  going  suffi- 
ciently far  back  into  the  past  we  find  it  in  a  condition  not 
unlike  the  primitive  nebula  which  Laplace  presupposed, 
with  the  exception  that  it  need  not  have  been  hot. 

320.  A  new  light  has  been  thrown  on  the  possible 
development  of  the  earth  and  moon  by  Professor  G.  H. 
Darwin's  study  of  the  effects  of  tidal  friction  (cf.  §  287  and 
§§  292,  293).  Since  the  tides  increase  the  length  of  the 
day  and  month  and  gradually  repel  the  moon  from  the 
earth,  it  follows  that  in  the  past  the  moon  was  nearer  to 
the  earth  than  now,  and  that  tidal  action  was  consequently 
much  greater.  Following  out  this  clue,  Professor  Darwin 
found,  by  a  series  of  elaborate  calculations  published  in 
1879-81,  strong  evidence  of  a  past  time  when  the  moon 
was  close  to  the  earth,  revolving  round  it  in  the  same  time 


§  320]  The  Evolution  of  the  Solar  System  409 

in  which  the  earth  rotated  on  its  axis,  which  was  then  a 
little  over  two  hours.  The  two  bodies,  in  fact,  were  moving 
as  if  they  were  connected ;  it  is  difficult  to  avoid  the 
probable  inference  that  at  an  earlier  stage  the  two  really 
were  one,  and  that  the  moon  is  in  reality  a  fragment  of  the 
earth  driven  off  from  it  by  the  too-rapid  spinning  of  the 
earth,  or  otherwise. 

Professor  Darwin  has  also  examined  the  possibility  of 
explaining  in  a  similar  way  the  formation  of  the  satellites 
of  the  other  planets  and  of  the  planets  themselves  from 
the  sun,  but  the  circumstances  of  the  moon-earth  system 
turn  out  to  be  exceptional,  and  tidal  influence  has  been 
less  effective  in  other  cases,  though  it  gives  a  satisfactory 
explanation  of  certain  peculiarities  of  the  planets  and  their 
satellites.  More  recently  (1892)  Dr.  See  has  applied  a 
somewhat  similar  line  of  reasoning  to  explain  by  means 
of  tidal  action  the  development  of  double  stars  from  an 
earlier  nebulous  condition. 

Speaking  generally,  we  may  say  that  the  outcome  of  the 
1 9th  century  study  of  the  problem  of  the  early  history 
of  the  solar  system  has  been  to  discredit  the  details  of 
Laplace's  hypothesis  in  a  variety  of  ways,  but  to  establish 
on  a  firmer  basis  the  general  view  that  the  solar  system 
has  been  formed  by  some  process  of  condensation  out  of 
an  earlier  very  diffused  mass  bearing  a  general  resemblance 
to  one  of  the  nebulae  which  the  telescope  shews  us,  and 
that  stars  other  than  the  sun  are  not  unlikely  to  have  been 
formed  in  a  somewhat  similar  way ;  and,  further,  the  theory 
of  tidal  friction  supplements  this  general  but  vague  theory, 
by  giving  a  rational  account  of  a  process  which  seems  to 
have  been  the  predominant  factor  in  the  development  of 
the  system  formed  by  our  own  earth  and  moon,  and  to  have 
had  at  any  rate  an  important  influence  in  a  number  cf 
other  cases. 


AUTHORITIES    AND    BOOKS    FOR    STUDENTS. 


I.  GENERAL. 

I  HAVE  made  great  use  throughout  of  R.  Wolfs  Geschichte  der 
Astronomie,  and  of  the  six  volumes  of  Delambre's  Histoire 
de  /'  Astronomic  (Ancienne,  2  vols.  ;  du  Moyen  Age,  I  vol. ; 
Moderne,  2  vols. ;  du  Dixhidtieme  Siecle,  I  vol.).  I  shall  subse- 
quently refer  to  these  books  simply  as  Wolf  and  Delambre 
respectively.  I  have  used  less  often  the  astronomical  sections 
of  Whewell's  History  of  the  Inductive  Sciences  (referred  to  as 
Whewell),  and  I  am  indebted — chiefly  for  dates  and  references 
— to  the  histories  of  mathematics  written  respectively  by  Marie, 
W.  W.  R.  Ball,  and  Cajori,  to  Poggendorffs  Handworterbuch 
der  Exacten  Wissenschaften,  and  to  articles  in  various  bio- 
graphical dictionaries,  encyclopaedias,  and  scientific  journals. 
Of  general  treatises  on  astronomy  Newcomb's  Popular  Astro- 
nomy, Young's  General  Astronomy,  and  Proctor's  Old  and  New 
Astronomy  have  been  the  most  useful  for  my  purposes. 

It  is  difficult  to  make  a  selection  among  the  very  large  number 
of  books  on  astronomy  which  are  adapted  to  the  general  reader. 
For  students  who  wish  for  an  introductory  account  of  astronomy 
the  Astronomer  Royal's  Primer  of  Astronomy  may  be  recom- 
mended ;  Young's  Elements  of  Astronomyis  a  little  more  advanced, 
and  Sir  R.  S.  Ball's  Story  of  the  Heavens,  Newcomb's  Popular 
Astronomy,  and  Proctor's  Old  and  New  Astronomy  enter  into 
the  subject  in  much  greater  detail.  Young's  General  Astronomy 
may  also  be  recommended  to  those  who  are  not  afraid  of  a 
little  mathematics.  There  are  also  three  modern  English  books 
dealing  generally  with  the  history  of  astronomy,  in  all  of  which 
the  biographical  element  is  much  more  prominent  than  in  this 
book  :  viz.  Sir  R.  S.  Ball's  Great  Astronomers,  Lodge's  Pioneers 
of  Science,  and  Morton's  Heroes  of  Science  :  Astronomers. 

411 


412  Authorities  and  Books  for  Students 

II.   SPECIAL  PERIODS. 

Chapters  1.  and  II.  —In  addition  to  the  general  histories  quoted 
above — especially  Wolf — I  have  made  most  use  of  Tannery's 
Recherches  sur  fHistoire  de  I  Astronomic  Ancienne  and  of  several 
biographical  articles  (chiefly  by  De  Morgan)  in  Smith's  Dictionary 
of  Classical  Biography  and  Mythology.  Ideler's  Chronologische 
Untersuchungen,  Hankel's  Geschichte  der  Mathematik  im  Altcr- 
thum  und  Mittelalter,  G.  C.  Lewis's  Astronomy  of  the  Ancients, 
and  Epping  &  Strassmaier's  Astronomisches  aus  Babylon  have 
also  been  used  to  some  extent.  Unfortunately  my  attention  was 
only  called  to  Susemihl's  Geschichte  der  Griechischen  Litteratur 
in  der  Alexandriner  Zeit  when  most  of  my  book  was  in  proof, 
and  I  have  consequently  been  able  to  make  but  little  use  of  it. 

I  have  in  general  made  no  attempt  to  consult  the  original 
Greek  authorities,  but  I  have  made  some  use  of  translations 
of  Aristarchus,  of  the  Almagest,  and  of  the  astronomical  writings 
of  Plato  and  Aristotle. 

Chapter  III. — The  account  of  Eastern  astronomy  is  based 
chiefly  on  Delambre,  and  on  Hankel's  Geschichte  der  Mathematik 
im  Altcrthum  und  Mittelalter\  to  a  less  extent  on  Whevvell. 
For  the  West  I  have  made  more  use  of  Whewell,  and  have 
borrowed  biographical  material  for  the  English  writers  from  the 
Dictionary  of  Rational  Biography.  I  have  also  consulted  a  good 
many  of  the  original  astronomical  books  referred  to  in  the  latter 
part  of  the  chapter. 

I  know  of  no  accessible  book  in  English  to  which  to  refer 
students  except  Whewell. 

Chapter  IV. — For  biographical  material,  for  information  as  to 
the  minor  writings,  and  as  to  the  history  of  the  publication  of 
the  De  Revolutionibus  I  have  used  little  but  Prowe's  elaborate 
Nicolaus  Coppernicus,  and  the  documents  printed  in  it.  My 
account  of  the  De  Revolutionists  is  taken  from  the  book  itself. 
The  portrait  is  taken  from  Dandeleau's  engraving  of  a  picture  in 
Lalande's  possession.  I  have  not  been  able  to  discover  any 
portrait  which  was  clearly  made  during  Coppernicus's  lifetime, 
but  the  close  resemblance  between  several  portraits  dating  from 
the  i/th  century  and  Dandeleau's  seems  to  shew  that  the  latter 
is  substantially  authentic. 

There  is  a  readable  account  of  Coppernicus,  as  well  as  of  several 
other  astronomers,  in  Bertrand's  Fondateurs  de  I Astronomie 
Moderne  ;  but  I  have  not  used  the  book  as  an  authority. 

Chapter  V  —  For  the  life  of  Tycho  I  have  relied  chiefly  on 
Dreyer's  Tycho  Brahe}  which  has  also  been  used  as  a  guide  to 
his  scientific  work  ;  but  I  have  made  constant  reference  to  the 
original  writings :  I  have  also  made  some  use  of  Gassendi's  Vita 


Authorities  and  Books  for  Students  413 

Ty chants  Brake.  The  portrait  is  a  reproduction  of  a  picture  in 
the  possession  of  Dr.  Crompton  of  Manchester,  described  by  him 
in  the  Memoirs  of  the  Manchester  Literary  and  Philosophical 
Society,  Vol.  VI.,  Ser.  III.  For  minor  Continental  writers  I  have 
i  sed  chiefly  Wolf  and  Delambre,  and  for  English  writers, 
Whewell,  various  articles  by  De  Morgan  quoted  by  him,  and 
articles  in  the  Dictionary  of  National  Biography. 

Students  will  find  in  Dreyer's  book  all  that  they  are  likely  to 
want  to  know  about  Tycho. 

Chapter  VI. — For  Galilei's  life  I  have  used  chiefly  Karl  von 
Gebler's  Galilei  und  die  Romische  Curie,  partly  in  the  original 
German  form  and  partly  in  the  later  English  edition  (translated 
by  Mrs.  Sturge).  For  the  disputed  questions  connected  with  the 
trial  I  have  relied  as  far  as  possible  on  the  original  documents 
preserved  in  the  Vatican,  which  have  been  published  by  von 
Gebler  and  independently  by  L'£pinois  in  Les  Pieces  du  Proces 
de  Galilee :  in  the  latter  book  some  of  the  most  important  docu- 
ments are  reproduced  in  facsimile.  For  personal  characteristics 
I  have  used  the  charming  Private  Life  of  Galileo,  compiled 
chiefly  from  his  correspondence  and  that  of  his  daughter  Marie 
Celeste.  I  have  also  read  with  great  interest  the  estimate  of 
Galilei's  work  contained  in  H.  Martin's  Galilee,  and  have  probably 
borrowed  from  it  to  some  extent.  What  I  have  said  about 
Galilei's  scientific  work  has  been  based  almost  entirely  on  study 
of  his  own  books,  either  in  the  original  or  in  translation  :  I  have 
used  freely  the  translations  of  the  Dialogue  on  the  Two  Chief 
Systems  of  the  World  and  of  the  Letter  to  the  Grand  Duchess 
Christine  by  Salusbury,  that  of  the  Two  New  Sciences  by 
Weston  (as  well  as  that  by  Salusbury),  and  that  of  the  Sidereal 
Messenger  by  Carlos.  I  have  also  made  some  use  of  various 
controversial  tracts  written  by  enemies  of  Galilei,  which  are  to  be 
found  (together  with  his  comments  on  them)  in  the  magnificent 
national  edition  of  his  works  now  in  course  of  publication  ;  and 
of  the  critical  account  of  Galilei's  contributions  to  dynamics 
contained  in  Mach's  Geschichte  der  Mechanik. 

Wolf  and  Delambre  have  only  been  used  to  a  very  small 
extent  in  this  chapter,  chiefly  for  the  minor  writers  who  are 
referred  to. 

The  portrait  is  a  reproduction  of  one  by  Sustermans  in  the 
Uffizi  Gallery. 

There  is  an  excellent  popular  account  of  Galilei's  life  and 
work  in  the  Lives  of  Eminent  Persons  published  by  the  Society 
for  die  Diffusion  of  Useful  Knowledge;  students  who  want 
fuller  accounts  of  Galilei's  life  should  read  Gebler's  book  and 
the  Private  Life,  which  have  been  already  quoted,  and  are 
strongly  recommended  to  read  at  any  rate  parts  of  the  Dialogue 


414  Authorities  and  Books  for  Students 

on  the  Two  Chief  Systems  of  the  World,  either  in  the  original  or 
in  the  picturesque  old  translation  by  Salusbury :  there  is  also  a 
modern  German  version  of  this  book,  as  well  as  of  the  Two  New 
Sciences,  in  Ostwald's  series  of  Klassiker  der  exakten  Wissen- 
schaften. 

Chapter  VIL— For  Kepler's  life  I  have  used  chiefly  Wolf 
and  the  life — or  rather  biographical  material — given  by  Frisch 
in  the  last  volume  of  his  edition  of  Kepler's  works,  also  to  a 
small  extent  Breitschwerdt's  Johann  Keppler.  For  Kepler's 
scientific  discoveries  I  have  used  chiefly  his  own  writings,  but  I 
am  indebted  to  some  extent  to  Wolf  and  Delambre,  especially 
for  information  with  regard  to  his  minor  works.  The  portrait 
is  a  reproduction  of  one  by  Nordling  given  in  Frisch's  edition. 

The  Lives  of  Eminent  Persons,  already  referred  to,  also  contains 
an  excellent  popular  account  of  Kepler's  life  and  work. 

Chapter  VIII. — I  have  used  chiefly  Wolf  and  Delambre ; 
for  the  English  writers  Gascoigne  and  Horrocks  I  have  used 
Whewell  and  articles  in  the  Diet.  Nat.  Biog.  What  I  have 
said  about  the  work  of  Huygens  is  taken  directly  from  the  books 
of  his  which  are  quoted  in  the  text ;  and  for  special  points  I 
have  consulted  the  Principia  of  Descartes,  and  a  very  few  of 
Cassini's  extensive  writings. 

There  is  no  obvious  book  to  recommend  to  students. 

Chapter  IX. — For  the  external  events  of  Newton's  life  I  have 
relied  chiefly  on  Brewster's  Memoirs  of  Sir  Isaac  Newton  ;  and 
for  the  history  of  the  growth  of  his  ideas  on  the  subject  of 
gravitation  I  have  made  extensive  use  of  W.  W.  R.  Ball's  Essay 
on  Newton's  Principia,  and  of  the  original  documents  contained 
in  it.  I  have  also  made  some  use  of  the  articles  on  Newton  in 
the  Encyclopaedia  Britannica  and  the  Dictionary  of  National 
Biography ;  as  well  as  of  Rigaud's  Correspondence  of  Scientific 
Men  of  the  Seventeenth  Century,  of  Edleston's  Correspondence 
of  Sir  Isaac  Newton  and  Prof.  Cotes,  and  of  Baily's  Account  of 
the  Rev*-  John  Flamsteed.  The  portrait  is  a  reproduction  of  one 
by  Kneller. 

Students  are  recommended  to  read  Brewster's  book,  quoted 
above,  or  the  abridged  Life  of  Sir  Isaac  Newton  by  the  same 
author.  The  Laws  of  Motion  are  discussed  in  most  modern 
text-books  of  dynamics ;  the  best  treatment  that  I  am  acquainted 
with  of  the  various  difficulties  connecte.d  with  them  is  in  an 
article  by  W.  H.  Macaulay  in  the  Bulletin  of  the  American 
Mathematical  Society,  Ser.  II.,  Vol.  III.,  No.  10,  July  1897. 

Chapter  X. — For  Flamsteed  I  have  used  chiefly  Baily's 
Account  of  the  Revd-  John  Flamsteed',  for  Bradley  little  but  the 
Miscellaneous  Works  and  Correspondence  of  the  Rev.  James 


Authorities  and  Books  for  Students  415 

Bradley  (edited  by  Rigaud),  from  which  the  portrait  has  been 
taken.  My  account  of  Halley's  work  is  based  to  a  considerable 
extent  on  his  own  writings  ;  there  is  a  good  deal  of  biographical 
information  about  him  in  the  books  already  quoted  in  connection 
with  Newton  and  Flamsteed,  and  there  is  a  useful  article  on 
him  in  the  Dictionary  of  National  Biography.  I  have  made 
a  good  deal  of  use  in  this  chapter  of  Wolf  and  Delambre, 
especially  in  dealing  with  Continental  astronomers  ;  and  for 
special  parts  of  the  subject  I  have  used  Grant's  History  *f 
Physical  Astronomy,  Todhunter's  History  of  the  Mathematical 
Theories  of  Attraction  and  the  Figure  of  the  Earth,  and 
Poynting's  Density  of  the  Earth. 

Chapter  XI. — Most  of  the  biographical  material  has  been 
taken  from  Wolf,  from  articles  in  various  encyclopaedias  and 
biographical  dictionaries,  chiefly  French,  and  from  Delambre's 
hloge  of  Lagrange.  The  two  portraits  are  taken  respectively 
from  Serret's  edition  of  the  Oeuvres  de  Lagrange  and  from 
the  Academy's  edition  of  the  Oeuvres  Completes  de  Laplace. 
Gautier's  Essai  Historique  sur  le  Probleme  des  Trois  Corps  and 
Grant's  History  of  Physical  Astronomy  have  been  the  books  most 
used  for  my  account  of  the  scientific  contributions  of  the  various 
astronomers  dealt  with;  I  have  also  consulted  various  modern 
treatises  on  gravitational  astronomy,  especially  Tisserand's 
Mecanique  Celeste,  Brown's  Lunar  Theory,  and  to  a  less  extent 
Cheyne's  Planetary  Theory  and  Airy's  Gravitation.  For  special 
points  I  have  used  Todhunter's  History,  already  referred  to. 
Of  the  original  writings  I  have  made  a  good  deal  of  use  of 
Laplace's  Mecanique  Celeste  as  well  as  of  his  Systeme  du  Monde ; 
I  have  also  consulted  a  certain  number  of  his  other  writings  and 
of  those  of  Lagrange  and  Clairaut ;  but  have  made  no  systematic 
study  of  them. 

Students  who  wish  to  know  more  about  gravitational  astronomy 
but  have  little  knowledge  of  mathematics  should  try  to  read 
Airy's  Gravitation ;  Herschel's  Outlines  of  Astronomy  and 
Grant's  History  (quoted  above)  also  deal  with  the  subject 
without  employing  mathematics,  and  are  tolerably  intelligible. 

Chapter  XII. — The  account  of  Herschel's  career  is  taken 
chiefly  from  Mrs.  John  Herschel's  Memoir  of  Caroline  Herschel^ 
from  Miss  A.  M.  Clerke's  The  Herschels  and  Modern  Astronomy, 
from  the  Popular  History  of  Astronomy  in  the  Nineteenth 
Century  by  the  same  author,  and  from  Holden's  Sir  William 
Herschel,  his  Life  and  Works.  The  last  three  books  and  the 
Synopsis  and  Subject  Index  to  the  Writings  of  Sir  William 
Herschel  by  Holden  &  Hastings  have  been  my  chief  guides  to 
Herschel's  long  series  of  papers  ;  but  nearly  everything  that  I 
have  said  about  his  chief  pieces  of  work  is  based  on  his  own 


4i 6  4uthorities  and  Books  for  Students 

writings.  I  have  made  also  some  little  use  of  Grant's  History 
(already  quoted),  of  Wolf,  and  of  Miss  Clerke's  System  of  the 
Stars. 

Students  are  recommended  to  read  any  or  all  of  the  first  four 
books  named  above ;  the  Memoir  gives  a  charming  picture  of 
Herschel's  personal  life  and  especially  of  his  relations  with  his 
sister.  There  is  also  a  good  critical  account  of  Herschel's  work 
on  sidereal  astronomy  in  Proctor's  Old  and  New  Astronomy. 

Chapter  XIII. — Except  in  the  articles  dealing  with  gravita- 
tional astronomy  I  have  constantly  used  Miss  Clerke's  History 
(already  quoted),  a  book  which  students  are  strongly  recom- 
mended to  read  ;  and  in  dealing  with  the  first  half  of  the  century 
I  have  been  helped  a  good  deal  by  Grant's  History.  But  for 
the  most  part  the  materials  for  the  chapter  have  been  drawn 
from  a  great  number  of  sources — consisting  very  largely  of  the 
original  writings  of  the  astronomers  referred  to — which  it  would 
be  difficult  and  hardly  worth  while  to  enumerate ;  for  the  lives 
of  astronomers  (especially  of  English  ones),  as  well  as  for  recent 
astronomical  history  generally,  I  have  been  much  helped  by  the 
obituary  notices  and  the  reports  on  the  progress  of  astronomy 
which  appear  annually  in  the  Monthly  Notices  of  the  Royal 
Astronomical  Society. 

I  add  the  names  of  a  few  books  which  deal  with  special  parts 
of  modern  astronomy  in  a  non-technical  way  : — 

The  Sun,  C.  A.  Young ;  The  Sun,  R.  A.  Proctor ;  The  Story 
of  the  Sun,  R.  S.  Bali ;  The  Suns  Place  in  Nature,  J.  N. 
Lockyer. 

The  Moon,  E.  Neison  ;   The  Moon,  T.  G.  Elger. 
Saturn  and  its  System,  R.  A.  Proctor. 
Mars,  Percival  Lowell. 

The  World  of  Comets,  A.  Guillemin  (a  well-illustrated  but 
uncritical  book,  now  rather  out  of  date)  ;  Remarkable 
Comets,  W.  T.  Lynn  (a  very  small  book  full  of  useful  in- 
formation) ;  The  Great  Meteoritic  Shower  of  November, 
W.  F.  Denning. 
The  Tides  and  Kindred  Phenomena  in  the  Solar  System,  G.  H. 

Darwin. 
Remarkable  Eclipses,  W.  T.  Lynn  (of  the  same  character  as 

his  book  on  Comets.) 
The  System  of  the  Stars,  A.  M.  Clerke. 

Spectrum  Analysis,  H.  Schellen ;  Spectrum  Analysis,  H.  E. 
Roscoe. 


INDEX   OF   NAMES. 

Roman  figures  refer  to  the  chapter 's,  Arabic  to  the  articles.  The 
numbers  given  in  brackets  after  the  name  of  an  astronomer  are 
the  dates  of  birth  and  death.  All  dates  are  A.D.  unless  otherwise 
stated.  In  cases  in  which  an  author  s  name  occurs  in  several 
articles,  the  numbers  of  the  articles  in  which  the  principal  account  of 
him  or  of  his  work  is  given  are  printed  in  clarendon  type  thus  :  286. 
The  names  of  living  astronomers  are  italicised. 


.  Abul  Wafa.     See  Wafa 
Adams  (1819-1892),  xm.  286, 

287,  289 

Adelard.     See  Athelard 
Airy   (1801-1892),   x.    227    «; 

xm.  281,292 
Albategnius  (7-929),  n.  53  ;  HI. 

59,  66,  68  n  ;  iv.  84,  85 
Albert  (of  Prussia),  v.  94 
Albertus  Magnus  (i3th  cent.), 

in.  67 

Alcuin  (735-804),  in.  65 
Alembert,  d'.     See  D'Alembert 
Alexander,  n.  31 
Alfonso  X.  (1223-1284),  in.  66, 

68 ;  v.  94 

Al  Mamun,  in.  57,  69 
Al  Mansur,  in.  56 
Al  Rasid,  in.  56 
Alva,  vii.  135 
Anaxagoras     (499     B.C.  ?-427 

B.C  ?),  i.  17 
Anaximander     (610     B.C.-546 

B.C.  ?),  i.  ii 
Apian  (1495-1552),  in.  69;  v. 

97  ;  vn.  146 


Apollonius  (latter  half  of  3rd 

cent.  B.C.),  ii.  38,  39>  45»  S*. 

52  n\  x.  205 
Arago,  xii.  254 
Archimedes,  n.  52  n  ;  HI.  62 
Argelander  (1799-1875),    xm. 

280 
Aristarchus  (earlier  part  of  3rd 

cent.  B.C.),  ii.  24,  32,  41,  42, 

54;  iv.  75 
Aristophanes,  ii.  19 
Aristotle   (384  B.C.-322  B.C.), 

11.24,  27-30,  31,  47,  5i,  52; 

HI.  56,  66,  67,  68  ;  iv.  70,  77 ; 

v.    100 ;    vi.    116,    121,  125, 

134;  viii.  163 
Aristyllus  (earlier  part  of  3rd 

cent.  B.C.),  ii.  32,  42 
Arzachel    UL    1080),    in.    61, 

66 
d'Ascoli,    Cecco    (i3th    cent.), 

in.  67 
Athelard    (beginning    of    I2th 

cent.),  in.  66 
Auzout     (7-1691),     vin.    155,' 

160 ;  x.  198 

417  27 


4i  8  Index  of  Names 

[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.'] 


Bacon,    Francis     (1561-1627), 

vi.  134;  vni.  163 
Bacon,     Roger    (12147-1294), 

in.  67;  vi.  118 
Bailly,  xi.  237 
Ball,  xin.  278  n 
Bar,  Reymers  (Ursus)  (?-i6oo), 

v.  105 
Barberini    (Urban    VIII.),    vi. 

125,  127,  131,  132 
Barnard,  xin.  294,  295 
Baronius,  vi.  125 
Barrow,  Isaac,  ix.  166 
Bayer,  xii.  266 
Bede,  in.  65 

Begh,  Ulugh.     See  Ulugh  Begh 
Bellarmine,  vi.  126 
Bentley,  ix.  191 
Berenice,  I.  12 
Bernouilli,  Daniel  (1700-1782), 

xi.  230 
Bernouilli,  James  (1654-1705), 

xi.  230 
Bernouilli,    John    (1667-1748), 

xi.  229,  230 
Bessel  (1784-1846),  x.   198  n, 

218;  xni.  272,  277-278,  279, 

280 

Bille,  v.  99 

Bliss  (1700-1764),  x.  219 
Bond,  William  Cranch  (1789- 

1859),  xni.  295 
Borelli  (1608-1679),  ix.  170 
Bouguer  (1698-1758),   x.   219, 

221 

Boulliau.     See  Bullialdus 
Bouvard,  xi.  247  n ;  xin.  289 
Bradley   (1693-1762),    X.    198, 

206-218,  219,  222-226;  xi. 

233;  xn.  257,  258,  263,  264; 

xni.  272,  273,  275,  277 
Brahe,  Tycho  (1546-1601),  in. 

60,  62  ;  v.  97,  98  n,  99-112  ; 

vi.  113,  117,  127;  vii.  136- 

139,  141  n,  142, 145,  146, 148  ; 


vni.  152,  153,  162;  ix.  190; 

x.  198,   203,   225;  xii.  257; 

xin.  275 

Brudzewski,  iv.  71 
Bruno,  vi.  132 

Bullialdus  (1605-1694),  xii.  266 
Bunsen,  xin.  299 
Burckhardt     (1773-1825),     XL 

241 

Burg  (1766-1834),  xi.  241 
Burgi  (1552-1632),  v.  97,  98; 

vin.  157 

Burney,  Miss,  xii.  260 
Burnham,  xin.  309 

Caccini,  vi.  125 
Caesar,  n.  21  ;  HI.  67 
Callippus  (4th   cent.  B.C.),    II. 

20,  26,  27 
Capella,  Martianus  (5th  or  6th 

cent.  A.D.),  iv.  75 
Carlyle,  xi.  232 
Carrington    (1826-1875),    xni. 

298,  302 

Cartesius.     See  Descartes 
Cassini,  Count  (1748-1845),  x. 

220 
Cassini,     Giovanni    Domenico 

(1625-1712),  vni.  160,  161; 

ix.   187;   x.   216,   220,  221, 

223  ;  xn.  253,  267  ;  xni.  297 
Cassini,    Jacques  (1677-1756), 

x.  220,  221,  222 
Cassini  de  Thury  (1714-1784), 

X.  220 

Castelli,  vi.  125 

Catherine  II.,  x.  227  ;  xi.  230, 

232 

Cavendish  (1731-1810),  x.  219 
Cecco   d'Ascoli    (12577-1327), 

in.  67 

Chandler,  xni.  285 
Charlemagne,  HI.  65 
Charles  II.,  x.  197,  223 
Chariots,  xni.  294 


Index  of  Names 


419 


\Roman  figures  refer  to  the  chapters^  Arabic  to  the  articles.'] 


Christian  (of  Denmark),  v.  106 
Christine  (the  Grand  Duchess), 

vi.  125 
Clairaut  (1713-1765),  xi.    229, 

230,  231,  232,  233-235,  237, 

239,  248  ;  xin.  290 
Clement  VII.,  iv.  73 
Clerke,  xm.  289  n 
Clifford,  ix.  173  n 
Colombe,   Ludovico   delle,  vi. 

119  n 

Columbus,  in.  68 
La  Condamine  (1701-1774),  x, 

219,  221 
Conti,  vi.  125 
Cook,  x.  227 
Coppernicus    (1473-1543),    n. 

24,  41  n,  54;  in.  55,  62,  69; 

IV.  passim ;  v.   93-97,    100, 

105,  1 10,  in  ;  vi.  117,   126, 

127,  129;  vn.   139,   150;  ix. 

186,  194;  xii.  257;  xin.  279 
Cornu,  xin.  283 
Cosmo  de  Medici,  vi.  121 
Cotes  (1682-1716),  ix.  192 
Crosthwait,  x.  198 
Cusa,  Nicholas  of  (1401-1464), 

iv.  75 

D'Alembert  (1717-1783),  x.  215; 

xi.  229,  230,  231  n,  232-235, 

237-239,  248 
Damoiseau   (1768-1846),    xin. 

286 

Dante,  ill.  67  ;  vi.  119  n 
Darwin,  xin.  292,  320 
Da  Vinci.     See  Vinci 
Dawes  (1799-1868),  xin.  295 
Delambre,  n.  44;   x.  218;  xi. 

247  n  ;  xm.  272 
Delaunay     (1816-1872),     xin. 

286,  287 

De  Morgan,  n.  52  n 
Descartes (1596-1650),  vin.  163 
Diderot,  xi.  232 


Digges,  Leonard  (7-1571  ?),  vi. 

118 

Digges,  Thomas  (?-i595),  v.  95 
Donati  (1826-1873),  xin.  304 
Doppler  (1803-1853),  xm.  302 
Dreyer,  xm.  308 
Duner,  xm.  302 

Ecphantus   (5th   or    6th   cent. 

B.C.),  ii.  24 
Eddin,  Nassir  (1201-1273),  m- 

62,  68  ;  iv.  73 
Encke    (1791-1865),    x.    227;; 

xm.  284 
Eratosthenes  (276  B.C.-I95  or 

196  B.C.),  n.  36,  45,  545  x- 

221 
Euclid  (fl.  300  B.C.),  n.  33,  52 

n  ;  in.  62,  66 ;   vi.   115;  ix. 

165 
Eudoxus  (409  B.C.  ?-356  B.C.  ?), 

n.  26,  27,  38,  42,  51 
Euler  (1707-1783),  x.  215,  226; 

xi.  229,  230,  231  «,  233-236, 

237,  239,  242,  243;  xm.  ;o/> 

Fabricius,  John  (1587-1615?), 

vi.  124 
Ferdinand  (the  Emperor),  vn. 

137,  H7 

Fernel  (1497-1558),  in.  69 
Ferrel,  xm.  287 
Field  (1525  7-1587),  v.  95 
Fizeau  (1819-1896),  xm.  283 
Flamsteed(i646-I72o),  ix.  192; 

x.  197, 198,  199,  204,  207  «, 

218,  225  ;  xii.  257  ;  xin.  275, 

281 
Fracastor  (1483-1553),  in.  69; 

iv.  89;  vn.  146 
Fraunhofer   (1787-1826),    xin. 

299,3u 

Frederick  II.  (of  Denmark),  v. 
101,  102,  106 


420 


Index  of  Names 


\Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Frederick   II.   (the    Emperor), 

in.  66 
Frederick  II.  (of  Prussia),  xi. 

230,  232,  237 

Galen,  n.  20;  HI.  56;  vi.  116 

Galilei,  Galileo  (1564-1642),  n. 
30  n,  47  ;  iv.  73  ;  v.  96,  98  n  ; 
VI.  passim;  VH.  135,  136, 
138,  145,  151  ;  viii.  152-154* 
157,  163;  ix.  165,  1 68,  170, 
I7i,  173.  179.  1 80,  1 86,  190, 
195;  x.  216;  xii.  253,  257, 
263,  268 ;  xin.  278,  295 

Galilei,  Vincenzo,  vi.  113 

Galle,  xin.  281,  289 

Gascoigne  (16127-1644),  vm. 
155,  156;  x.  198 

Gauss  (1777-1855),  xm.  275, 
276,  294 

Gautier  (1793-1881),  xin.  298 

Genghis  Khan,  HI.  62 

George  III.,  xii.  254-256 

Gerbert  (?-ioo3),  HI.  66 

Gherardo  of  Cremona  (1114- 
1187),  in.  66 

Gibbon,  n.  53  n 

Giese,  iv.  74 

Gilbert  (1540-1603),  VH.  150 

Gill,  xm.  280,  281 

Glaisher,  XHI.  289  n 

Godin  (1704-1760),  x.  221 

Goodricke  (1764-1786),  xii. 
266 

Grant,  xm.  289  n 

Grassi,  vi.  127 

Gregory,  James  (1638-1675), 
ix.  168,  169;  x.  202 

Gregory  XIII. ,  n.  22 

Gylden  (1841-1896),  xin.  288 

Hainzel,  v.  99 
Hi  I  \  xm.  301 
Halifax,  John.  See  Sacrobosco 


Halifax  (Marquis  of),  ix.  191 

Hall,  xm.  283  n,  295 

Halley  (1656-1742),  vm.  156; 
ix.  176,  177,  192  n  ;  x.  198, 
199-205,  206,  216,  223,  224, 
227;  XL  231,  233,  235,  243; 
xii.  265  ;  xm.  287,  290 

Hansen  (1795-1874),  xm.  282, 
284,  286,  290 

Harkness,  xm.  301 

Harriot  (1560-1621),  vi.  118, 
124 

Harrison,  x.  226 

Harun  al  Rasid,  HI.  56 

Helmholtz    (1821-1894),    xm. 

3r9 

Hencke  (1793-1866),  xin.  294 
Henderson   (1798-1844),    xm. 

279 
Heraclitus  (5th  cent.  B.C.),  n. 

24 

Herschel,  Alexander,  xn.  251 
Herschel,  Caroline  ( 1 7  50- 1 848), 

xii.  251,  254-256,  260 
Herschel,    John    (1792-1871), 

i.   12  ;  x.  221  ;   xi.  242;  xn. 

256;  xm.   289  n,  306-308, 

309,  316,  317,  319 
Herschel,  William  (1738-1822), 

ix.  168  ;  x.  223,  227  ;  xi.  250 ; 

XII.  passim  ;  xm.  272,  273, 

294,  296,  306-311,  317,  318 
Hesiod,  n.  19,  20 
Hevel  (1611-1687),   vm.  153; 

x.  198  ;  xn.  268 
Hicetas  (6th  or  5th  cent.  B.C.), 

n.  24;  iv.  75 

Hill,  xi.  233  n  ;  xm.  286,  290 
Hipparchus  (2nd  cent.  B.C.),  I. 

13;  n.  25,  27,  31,  32,  37-44, 

45,  47-52,  54 ;    in.  63,  68 ; 

iv.  73,  84;  v.  in  ;  vii.  145 
Hippocrates,  HI.  56 
Holwarda  (1618-1651),  xii.  266 
Holywood.     See  Sacrobosco 


Index  of  Names 


421 


\Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Honein  ben  Ishak  (?-873),  in. 

56 
Hooke    (1635-1703),    ix.   174, 

176}    X.  207,  212 

Horky,  vi.  121 

Horrocks    (1617  ?-i64i),    vm. 

156;  ix.  183;  x.  204 
Howlett,  xin.  298 
Huggins,  xin.  301,  304,  311- 

3*3 

Hulagu  Khan,  in.  62 
Humboldt,  xin.  298 
Hutton  (1737-1823),  x.  219 
Huygens  (1629-1695),  v.  98  n\ 
vi.  123  ;  vm.  154,  155,  157, 
158;  ix.  170-172,  191 
Hypatia  (?-4i5).  n-  53 


Ibn  Yunos.     See  Yunos 
Ishak    ben    Honein   (7-910  or 
911),  in.  56 

James  I.,  v.  102  ;  vii.  147 
James  II.,  ix.  192 
Janssen,  xin.  301,  307  n 
Joachim.     See  Rheticus 

Kaas,  v.  106 

Kant,   xi.   250  ;  xn.   258,  260  ; 
xin.  287 

Kapteyn,  xin.  280 

Kelvin,  xm.  292 

Kepler  (157  1  -1630),  n.  23,51  n,- 
54  ;  iv.  91  ;  v.  94,  100,  104, 
108-110;  vi.  113,  121,  130, 
132  ;  VII.  passim  ;  vm.  152, 
156,  1  60;  ix.  168-170,  172, 
175,  176,  190,  194,  195  ;  x. 
202,  205,  220  ;  xi.  228,  244  ; 
xm.  294,  301,  309 

Kirchhoff    (1824-1887),     xin. 

299,300,3ii 

Kirkwood    (1815-1895),     xin. 
294,  297 


Koppernigk,  iv.  71 

Korra,  Tabit  ben.     See  Tabit 

Lacaille  (1713-1762),  x.   222- 

224,  225,  227  ;  xi.  230,  233, 

235  ;  xn.  257,  259 
La  Condamine  (1701-1774),  x. 

219,  221 
Lagrange(  1736- 1813),  ix.  193; 

xi.   229,  231    n,  233  n,  236, 

237,  238-240,  242-245,  247, 

248;  xn.  251  ;  xm.  293,  294 
Lalande  (1732-1807),  xi.  235, 

241,  247  n  ;  xii.  265 
Lambert  (1728-1777),  XT.  243;, 

xn.  265 

Lami,  ix.  180  n 
Landgrave     of    Hesse.        See 

William  IV. 
Lang ley ,  xm.  307 
Lansberg  (1561-1632),  vm.  156 
Laplace   (1749-1827),  xi.   229, 
31   n,  238-248,  250;    xn. 

251,  256  ;  xm.  272,  273,  282, 

286-288,  290,  293,  297,  318- 

320 
Lassell  (1799-1880),  xii.  267  ; 

xm.  295 

Lavoisier,  xi.  237 
Legendre     (1752-1833),     xm. 

275,  276 

Leibniz,  ix.  191,  193 
Lemaire,  xn.  255 
Leverrier  (1811-1877),  xm.  282, 

284,  288,  289,  290,  293,  294 
Lexell  (1740-1784),  xn.  253 
Lindenau,  xi.  247  n 
Lionardo  da  Vinci.    See  Vinci 
Lippersheim  (?-i6i9),  vi.   118 
Locke,  ix.  191 
Lockyer,  xm.  301,  302 
Loewy,  xm.  283  n 
Louis  XIV.,  vm.  160 
Louis  XVI.,  xi.  237 
Louville  (1671-1732),  xi.  229 


422 


Index  of  Names 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles  J 


Lubbock  (1803-1865),  xm.  286, 

292 
Luther,  iv.  73 ;  v.  93 

Machin  (7-1751),  x.  214 
Maclaurin  (1698-1746),  x.  196  ; 

xi.  230,  231  ;  xn.  251 
Maestlin,  vn.  135 
Maraldi,  x.  220 
Marius  (1570-1624),  vi.    118; 

vii.  145 
Martianus       Capella.         See 

Capella 
Maskelyne  (1732-1811),  x.  219; 

xii.  254,  265 
Mason    (1730-1787),    x.    226; 

xi.  241 
Matthias   (the    Emperor),    vii. 

143,  147 
Maupertuis  (1698-1759),  x.  213, 

221  ;  xi.  229,  231 
Maxwell  (1831-1879),  xm.  297 
Mayer,  Tobias  (1723-1762),  x. 

217,  225,  226;  xi.  233,  241  ; 

xn.  265 

Melanchthon,  iv.  73,  74  ;  v.  93 
Messier  (1730-1817),  xii.  259, 

260 

Meton  (460  B.C.  ?-?),  n.  20 
Michel  Angelo,  vi.  113 
Michell,   John  (1724-1793),  x. 

219;  xii.  263,  264 
Michekon,  xm.  283 
Molyneux  (1689-1728),  X.  207 
Montanari  (1632-1687),  xn.  266 
Miiller.     See  Regiomontanus 

Napier,  v.  97  n 
Napoleon  I.,  xi.  238  ;  xn.  256 
Napoleon,  Lucien,  xi.  238  n 
Nassir     Eddin.       See     Eddin, 

Nassir 
Newcomb,  x.  227  n  \  xm.  283, 

286,  290 


Newton   (1643-1727),    n.     54; 

iv.    75;    vi.    130,    133,    134; 

vn.  144,  150;  vm.  152;  IX. 

passim;     x.     196-200,     211, 

213,  215-217,   219,  221;  xi. 

228,  229,  231-235,  238,  249; 

xii.  257  ;  xm.  273,  299 
Niccolini,  vi.  132 
Nicholas  of  Cusa  (1401-1464), 

iv.  75 

Nonius  (1492-1577),  m.  69 
Norwood   (15907-1675),    vin. 

159;  ix.  173 
Numa,  n.  21 
Nunez.     See  Nonius 
Nyren,  xm.  283  n 

Olbers  (1758-1840),  xm.  294 
Orange,  Prince  of,  v.  107 
Osiander,  iv.  74 ;  v.  93 

Palisa,  xm.  294 

Palitzsch  (1723-1788),  xi.  231 

Pemberton,  ix.  192 

Philolaus  (5th  cent.   B.C.),    n. 

24 ;  iv.  75 

Piazzi  (1746-1826),  xm.  294 
Picard  (1620-1682),  vm.    155, 

157,  159-161,  162;  ix.  174; 

X.   196,    198,  221 

Pickering,  xm.  314,  316 
Plana  (1781-1869),  xm.  286 
Plato  (428  B.c.7-347  B.C.?),  n. 

24,  25,  26,  5 1  ;  iv.  70 
Plato  of  Tivoli  (fl.   in6),  in. 

66 

Pliny  (23  A.D.-79  A.D.),  n.  45 
Plutarch,  n.  24  ;  xm.  301 
Pogson  (1829-1891),  xm.  316 
Poincare,  xm.  288 
Poisson  (1781-1840),  xm.  286, 

293 
Pontecoulant  (1795-1874),  xm. 

286 
Porta,  vi.  118 


Index  of  Names 


423 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles^ 


Posidonius(i35  B.C.  ?-$!  B.C.?), 

n-  45.  47 
Pouillet  (1791-1868),  xiu.  307, 

3*9 

Pound,  x.  206,  216 
Pr6vost  (1751-1839),  xii.  265 
Pritchard    (1808-1893),      xiu. 

278  n,  279,  316 
Ptolemy,  Claudius  (jft.  I4OA.D.), 

n.  25,  27,  32,  37,  46-52,  53, 

54;    in.  55,   57,  59-63,   68  ; 

iv.  70,  76,  80,  83-87,  89,  91  ; 

v.  94,  105  ;  vi.  121,  129,  134  ; 

vn.  145  ;  vin.  161  ;  ix.  194 ; 

x.  205  ;  XL  236 
Ptolemy  Philadelphia,  n.  31 
Purbach  (1423-1461),   in.  68; 

iv.  71 
Pythagoras  (6th  cent.   B.C.),  I. 

11,  14;  n.  23,  28,  47,  51,  54 

Recorde  (1510-1558),  v.  95 
Regiomontanus      (1436-1476), 

in.  68,  69;  iv.  70,  71  ;  v.  97, 

no 

Reimarus.     See  Bar 
Reinhold  (1511-1553),  v.   93- 

96;  vii.  139 
Reymers.     See  Bar 
Rheticus   (1514-1576),    iv.   73, 

74 ;  v.  93,  94,  96 
Ricardo,  n.  47  n 
Riccioli  (1598-1671),  vin.  153 
Richer  (7-1696),  vm.  161 ;  ix. 

1 80,  187  ;  x.  199,  221 
Rigaud,  x.  206  n 
Roemer(i644-I7io),  vm.  162 ; 

x.   198,    210,  216,  220,  225; 

xiu.  283 
Rosse   (1800-1867),   xm.   310, 

317 
Rothmann   (fl.     1580),   v.    97, 

98,  1 06 
Rudolph  II.  (the  Emperor),  v.. 

106-108;  vn.  138,  142,  143 


Sabine  ( 1788- 1883),  xiu.  298 
Sacrobosco  (7-1256?),  in.  67, 

68 

St.  Pierre,  x.  197 
Savary  (1797-1841),  xiu. 
Scheiner  (1575-1650),  vi. 

125;    vn.   138;    vm.    153; 

xn.  268 

Schiaparelli,  xili.  297 
Schomberg,  iv.  73 
Schoner,  iv.  74 
Schonfeld     (1828-1891),     xiu. 

280 
Schroeter(  1 745-1816),  xn.  267, 

271 

Schwabe  (1789-1875),  xm.  298 
Secchi  (1818-1878),  xm.  311, 

312 

See,  xm.  320 

Seleucus  (2nd  cent.  B.C.),  n.  24 
Shakespeare,  vi.  113 
Sharp  (1651-1742),  x.  198 
Slusius,  ix.  169 
Smith,  xn.  251 
Snell   (1591-1626),    vm.    159; 

ix.  173 

Sosigenes  (fl.  45  B.C.),  n.  21 
South  (1785-1867),  xm.  306 
Struve,  F.  G.  W.  (1793-1864), 

xm.  279,  309 
Struve,  O.,  xm.  283  n 
Svanberg  (1771-1851),  x.  221 
Sylvester  II.     See  Gerbert 

Tabit  ben  Korra  (836-901),  ill. 

56,  58,  68  ;  iv.  84 
Tamerlane,  in.  63 
Tannery,  n.  36  n 
Thales  (640   B.C.  ?~546   B.C.  ?), 

n.  23;  in.  55 
Theon  (fl.  365  A.D.),  n.  53 
Theophrastus,  II.  24 
Theophylactus,  iv.  72 
Thomson,  T.,  x.  208  n 
Thomson,  William.  See  Kelvin 


424 


Index  of  Names 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles  ] 


Thury,  Cassini  de.    See  Cassini 

de  Thury 
Timocharis  (beginning  of  3rd 

cent.  B.C.).  ii.  32,  42  ;  iv.  84 
Tycho  Brahe.     See  Brahe 

Ulugh  Begh   (1394-1449),   in. 

63,  68  ;  iv.  73 
Urban    VIII.    (Barberini),    vi. 

125,  127,  131,  132 
Ursus.     See  Bar 

Varignon,  ix.  180  n 

Vinci,  Lionardoda(i452-i5i9), 

in.  69 

Vogel,  xni.  313,  314 
Voltaire,  n.  21  ;  xi.  229 

Wafa,  Abul  (939  or  940-998), 
in.  60,  68  n  ;  iv.  85  ;  v.  1 1 1 

Wallenstein,  vn.  149 

Walther  (1430-1504),  in.  68; 
v.  97 


Wargentin  (1717-1783),  x.  216 

Watzelrode,  iv.  71 

Wefa.     See  Wafa 

Welser,  vi.  124 

Whewell  (1794-1866),  xni.  292 

William    IV.     (Landgrave    of 

Hesse)   (1532-1592),   v.   97, 

98,  too,  105,  106,  1 10 
Wilson  (1714-1786),  xii.  268; 

xni.  298 

Wolf,  Max,  xin.  294 
Wolf,  Rudolf  (1816-1893),  xin. 

298 
Wollaston    (1766-1828),     xm. 

299 

Wren  (1632-1723),  ix.  174,  176 
Wright,   Thomas  (1711-1786), 

xn.  258,  265 

Young,  xm.  301 
Yunos,  Ibn  ( ?-ioo8),  in.  60 
62,  68  n 

von  Zach,  xi.  247  n 


GENERAL    INDEX. 


Roman  figures  refer  to  the  chapters.  Arabic  to  the  articles.  When  several 
articles  are  given  under  one  heading  the  numbers  of  the  most  important 
are  printed  in  clarendon  type,  thus  :  207.  The  names  of  books  are 
printed  in  italics. 


Aberration,  x.  206,  207-211,  212, 
213,  216,  218;  xn.  263;  xin. 
277,  283,  284 

Academic  Francaise,  xi.  232,  238 
Academy  of  Berlin,  xi.  230,  237 
Academy   of  St.  Petersburg,   xi. 

230,  233 
Academy  of  Sciences  (of  Paris), 

X.       221,      223;      XI.       229-233, 

235-237 

Academy  of  Turin,  xi.  237,  238 
Acceleration,    vi.    133;    ix.    171, 

172,    173.    '79i    l8o»    185,    195; 

x.  223 
Ad  Vitellionem  Paralipomena  (of 

Kepler),  vn.  138 

Alaesive  Scalae  (of  Digges),  v.  95 
Aldebaran,  in.  64;  xin.  316  n 
Alexandrine  school,  n.  21,  31-33, 

36-38,  45,  53 
Alfonsine   Tables,  in.  66,   68;  v. 

94,  96,  99 

Algol,  xn.  266;  xni.  314,  315 
Almagest  (of  Ptolemy),  n.  46-52  ; 

"i-  55,  56>  58»  6o»  62,  66,  68; 

iv.  75,  76,  83 

Almagest  (of  Abul  Wafa),  in.  60 
Almagest,  New  (of  Kepler),  vn. 

148 
Almagest,  New  (of  Riccioli),  vin. 

'53 

425 


Almanac,  Nautical,    x.  218;  xin. 

286,  288,  290 
Almanacks,  I.  1 8  n  ;  11.  20,  38 ;  in. 

64,   68;   v.  94,   95,    100;    vn. 

136;  x.   218,   224;    xin.    286, 

288,  290 

Altair,  in.  64;  xin.  316  n 
Analysis,  analytical  methods,  x. 

196 ;  xi.  234 

Angles,  measurement  of,  i.  7 
Annual  equation,  v.  Ill;  vn.  145 
Annual  motion  of  the  earth.     See 

Earth,  revolution  of 
Annual  motion  of  the  sun.     See 

Sun,  motion  of 
Annual  parallax.     See  Parallax, 

stellar 

Annular  eclipse,  n.  43;  vn.  145 
Anomalistic  month,  11.  40 
'  A.VTi'x.d&v,  ii.  24 
Apex  of  solar  motion,  xii.  265 
Aphelion,  iv.  85 
Apogee,  n.  39,  40,  48 ;  HI.  58,  59 ; 

iv.  85;    v.    in  ;  ix.    184-    xi. 

233 

Apparent  distance,  i.  7 
Apple,  Newton's,  ix.  170 
Apse,  apse-line,  11.  39,  40,  48 ;  iv. 

85 ;  ix.  183 ;  xi.  235,  236,  242, 

246 
Arabic  numerals,  in.  64 ;  v.  96 


426 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Arabs,  Arab  astronomy,  n.  46,  53; 

in.  56-61,  64,  66,  68;  v.  no; 

vin.  159;  xii.  266 
Arctic  regions,  n.  35 
Arcturus,  xii.  258 
Aries,  first  point  of  ( T  ),  i.  13  ; 

ii.     33,   42;  iv.    83   «;    v.    98, 

ill  ;  x.  198 

Asteroids.     See  Minor  planets 
Astrolabe,  n.  49;  in.  66 
Astrology,   i.    16,  18;  in.  56;  v. 

99,  100;  vn.  136,  149,  151 
Astronomiae     Fundamenta      (of 

Lacaille),  x.  224 
Astronomiae  Instauratae  Mecha- 

nica  (of  Tycho),  v.  107 
Astronomiae  Instauratae  Progvm- 

nasmata  (of  Tycho),  v.  104 
Astronomical    Society,    German, 

xin.  280 
Astronomical  Society,  Royal,  xii. 

256,  263 
Astt-onomicum     Caesareum      (of 

Apian),  v.  97 

Astronomisches  Jahrbuch,  xn.  253 
Astronomy,  divisions  of,  xin.  272 
Astronomy,  descriptive,  xin.  272, 

273.  294 
Astronomy,  gravitational,  x.  196  ; 

xin.  272,  273,  286 
Astronomy,    observational,    xin. 

272,  273 

Astronomy,  origin  of,  I.  2 
Astronomy,  scope  of,  I.  I 
Attraction.     See  Gravitation 
Autumnal    equinox,    i.    II.     See 

also  Equinox 

Axioms.    See  Laws  of  Motion 
Axis  (of  an  ellipse),  xi.  236,  244, 

245 

Babylonians.     See  Chaldaeans 
Bagdad,  in.  56,  57,  60,  68 
Belts  of  Jupiter,  xn.  267 
Betelgeux,  in.  64 
Biela's  comet,  xin.  305 
Binary  stars.     See  Stars,  double 
and  multiple 


Bode's  Astronomisches  Jahrbuch, 

xii.  253 

Bodily  tides,  xin.  292,  293 
Brightness  of  stars.     See  Stars, 

brightness  of 
Brooks's  comet,  xin.  305 
Brucia,  xni.  294 
Bureau  des  Longitudes,  xi.  238., 

Cairo,  in.  60 

Calculus  of  Variations,  xi.  237  n 

Calendar,  Greek,  11.  19,  20,  21 

Calendar,  Gregorian,  11.  22 ;  ix. 
165  n  ;  x.  217 

Calendar,  Julian,  11.  21,  22;  111. 
68;  iv.  73;  ix.  165  n;  x. 
197  «,  217 

Calendar,  Mahometan,  in.  56 

Calendar,  Roman,  11.  21 

Caliphs,  in.  56,  57,  69 

Canals  of  Mars,  xni.  297 

Cartesianism,  vin.  163;  IX.  191, 
195  ;  xi.  229 

Castor,  xii.  263,  264,  266 

Catalogues  of  stars.  See  Star- 
catalogues 

Cavendish  experiment,  x.  219 

Celestial  latitude.  See  Latitude, 
celestial 

Celestial  longitude.  See  Longi- 
tude, celestial 

Celestial  sphere,  i.  7,  8,  9-11,  13, 
14  ;  n.  24,  26,  33,  38-40,  45,  47, 
51  ;  m.  64,  67;  iv.  78,  80,  83, 
88;  v.  98,  105;  vi.  129;  vm. 
157  ;  x.  198,  207,  208,  214;  xii. 
257;  xin.  272 

Celestial  sphere,  daily  motion  of. 
See  Daily  motion 

Celestial  spheres,  n.  23,  26,  27,  38, 
51,  54;  in.  62,  68;  v.  100,  103 

Centre  of  gravity,  ix.  1 86 

Centrifugal  force,  vin.  158*2 

Ceres,  xin.  276,  294 

Chaldaeans  (Babylonians),  Chal- 
daean  astronomy,  i.  6,  1 1,  12, 
16-18;  ii.  30,  34,  40,  51,  54; 
in.  56 


General  Index 


427 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.'} 


Chart,  photographic,  xm.  280 
Chemistry  of  the  sun,  xiu.  299- 

301,  303 

Chinese  astronomy,  i.  6,  1 1 
Chords,  ii.  47  n 
Chromosphere,  x.  205  ;  xm.  301, 

3°3 

Chronometer,  x.  226 
Circular  motion,  n.  25,  26,  38,  51  ;    i 

iv.  76;  vn.  139;  vm.  158;  ix.    i 

171-173.     See  also   Eccentric,    i 

Epicycle 

Circumpolar  stars,  i.  9 ;  n.  35 
Clock.     See  Pendulum  clock  and 

Chronometer 
Clustering  power,  xn.  261.     See 

also  Condensation  of  nebulae 
Coelum  Australe   Stelliferum    (of 

Lacaille),  x.  223 
Collimation  error,  x.  225  n 
Comets,  i.  i  ;  n.  30  ;  in.  68,  69  ;  v. 

100,  103-105;  vi.  127,  129;  vii. 

144,    146;   vm.   153;   ix.   190, 

192 ;  x.  200,  205,  217,  224;  xi. 

228,  231,   243,   248,  250;   xii. 

253,  256,  259;  xm.  272,  291, 

304,  305,  307 
Comet,  Biela's,  xm.  305 
Comet,  Brooks's,  xm.  305 
Comet,  Encke's,  xm.  291 
Comet,  Halley's,  vii.  146;  x.  200, 

205  ;  xi.  231,  232 ;  xm.  291,  307 
Comet,     Lexell's,    xi.   248;    xm. 

305 

Comet,  Olbers's,  xm.  291 
Comet,  Pons-Brooks,  xm.  291 
Comet,  Tebbutt's,  xm.  305 
Comet,  Tuttle's,  xm.  291 
Cometographia    (of  Hevel),    vm. 

'S3 

Commentaries  on  the  Motions   of 

Mars  (of  Kepler),  vn.  135  «,  139, 

141,  150;* 
ComiJientarwlus(o{Coppermcus), 

iv.  37 ;  v.  100 
Compleat  System    of    Optics   (of 

Smith),  xn.  251 
Complete  induction,  ix.  195 


Condensation  of  nebulae,  xi.25O; 

xn.  261  ;  xm.  318 
Conic,  conic   section,  vn.  140  n ; 

xm.  309 
Conjunction,  n.  43,  48  n  ;  m.  60  ; 

v.  1 10,  in  ;  x.  227 
Conservation  of  energy,  xm.  319 
Constant  of  aberration,  x.  209, 2 10; 

xm.  283  n 
Constellations,  i.   12,   13;   n.  2O, 

26,  34,  42  ;  x.  223 
Construction  of  the  heavens,  xn. 

257.     See  also  Sidereal  system, 

structure  of 
Corona,   vn.    145 ;   x.   205 ;  xm. 

301,  303 

Counter-earth,  n.  24 
Crape-ring,  xn.  267  ;  xm.  295 
Craters  (on  the  moon),  vm.  153; 

xm.  296 
Curvature    of    the    earth.      See 

Earth,  shape  of 

Daily  Motion  (of  the  celestial 
sphere),  i.  5,  8,  9,  10 ;  n.  23,  24, 
26,  33,  38,  39,  46,  47 ;  m.  67, 
68 ;  iv.  78,  80,  83 ;  v.  98,  105  ; 
vi.  129;  vm.  157 

D'Alembert's  principle,  xi.  232, 
237  n 

Damascus,  in.  57 

Darlegung  (of  Hansen),  xm.  286 

Day,  i.  4,  11,16;  11.47;  xm.  287, 
293,  320 

Day-and-night,  i.  i6« 

Day-hour,  i.  16 

Declination,  11.  33,  35,  39;  x.  213, 
218;  xm.  276 

Declination  circle,  11.  33 

De  Coelo  (of  Aristotle),  n.  27 

Deductive    method,    inverse,    ix. 

'95 
Deferent,  n.  39,  48,  51;  HI.  68 ; 

iv.  86,  87 
Degree,  i.  7 
Deimos,  xm.  295 
De    Magnete    (of    Gilbert),    vii. 

150 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


De  Motu  (of  Newton),  ix.  177, 
191 

De  Mundi  aetherei  (of  T/cho), 
v.  104 

De  Nova  Stella  (of  Tycho),  v.  100 

De  Revolutionibus  (of  Copperni- 
cus),  n.  41  n ;  iv.  74-92;  v.  93, 
94;  vi.  126 

De  Saturni  Luna  (of  Huygens), 
viu.  154 

Descriptive  astronomy,  xm.  272, 
273»  294 

Deviation  error,  x.  225  n 

Dialogue  on  the  Two  Chief  Sys- 
tems (of  Galilei),  vi.  124  n, 
128-132,  133 

Differential  method  of  parallax, 
vi.  129 ;  xn.  263  ;  xm.  278 

Diffraction-grating,  xm.  299 

Dione,  vm.  160 

Dioptrice  (of  Kepler),  vn.  138 

Direct  motion,  i.  14 

Disturbing  force.  See  Perturba- 
tions 

Diurnal  method  of  parallax,  xm. 
281,  284 

Doctrine  of  the  sphere.  See 
Spherics 

Doppler's    principle,     xm.    302, 

313,  3H 

Double  hour,  i.  16 
Double-star  method  of  parallax. 

See     Differential     method      of 

parallax 
Double  stars.     See  Stars,  double 

and  multiple 

Draconitic  month,  n.  40,  43 
Durchmusterung,  xm.  280 
Dynamics,  vi.   133,   134;  ix.   179, 

180;  xi.  230,  232,  237 
Dynamique,  fraitede  (of  D'Alem- 

bert),  xi.  232 

Earth,  i.  i,  15,  17;  n.  28,  29,  32, 
39,  41,  43,  47,  49,  51  ;  m.  66, 
69;  iv.  80,  86;  vi.  117,  121, 
133;  vii.  136  n.  144,  145,  150; 
vm.  153,  1 54;  ix.  173,  174,  179- 


182,    184,   1 86,    195 ;    xi.    228, 

245  ;  xm.   285,  287,  292,  293, 

297,  320.    See  also  the  following 

headings 
Earth,  density,  mass  of,  ix.  180, 

185,    189;    x.    219;    xi.    235; 

xm.  282,  294 
Earth,  motion  of,  n.  24,  32,  47  ; 

iv.  73,  76,  77 ;  v.  96,  97,  105  ; 

vi.  121,  125-127,129-132;  vm. 

161,  162;  ix.  186, 194;  xn.  257. 

See  also  Earth,  revolution  oiand 

rotation  of 
Earth,  revolution  of,annual  motion 

of,  ii.  23,  24,  28  n,  30,  47  ;  iv.  75, 

77,  79-82,  85-88,  89,  90,  92;  v. 

in  ;  vi.  119,  126,  129,  131,  133  ; 

vn.  139,  142,  146 ;  vm.  161  ;  ix. 

172,  183  ;  x.  207-210,  212,  227 ; 

xi.  235,  236,  240 ;  xii.  263 ;  xm. 

278,  282,  283 

Earth,  rigidity  of,  xm.  285,  292 
Earth,  rotation  of,   daily  motion 

of,  11.  23,  24,  28  n  ;  iv.  75,  78, 

79  n,  80,  84;  v.  105;  vi.   124, 

126,   129,    130;    ix.    174,   194; 

x.  206,  207,  213  ;  xm.  281,  285, 

287,  320 
Earth,  shape  of,  n.  23,  29,  35, 

45,  47,  54;  iv.  76;  vm.  161; 

ix.  187,  1 88;  x.  196,  213,  215, 

220,  221,  222,  223 ;  xi.  229,  231, 
237,  248 

Earth,  size  of,  n.  36,  41,  45,  47, 
49;  I"-  57,  69;  iv.  85;  vn.  145; 
vm.  159,  161  ;  ix.  173,  174;  x. 

221,  222,  223 

Earth,  zones  of,  n.  35,  47 
Earthshine,  m.  69 
Easter,  rule  for  fixing,  n.  2O 
Eccentric,  n.  37,  39,  40,  41    48, 
51 ;  m.  59  ;  iv.  85,  89-91 ;  vn. 

139,  15° 

Eccentricity,  n.  39 ;    iv.  85 ;  vn. 
140  n ;  xi.  228,  236,  240,  244- 
246,  250;  xm.  294,  318 
Eccentricity  fund,  xi.  245 
Eclipses,  i.  11,  15,  17;  11.  29,  32, 


General  Index 
[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.'] 


429 


40-42,  43,  47-49,  54;  in.  57, 
68  ;  iv.  76,  85  ;  v.  1 10 ;  vi.  127 ; 
vii.  145,  148;  viu.  162;  x.  201, 
205,  210,  216,  227;  xi.  240; 
xni.  287,  301 

Eclipses,  annular,  n.  43  ;  vii.  145 

Eclipses,  partial,  n.  43 

Eclipses,  total,  n.  43 ;  vn.  145  ; 
x.  205  ;  xin.  301 

Ecliptic,  i.  11,  13,  14;  ii.  26,  33, 
35.  36,  38,  40,  42,51;  ni.  58, 
59,  68 ;  iv.  80,  82-84,  87,  89 ; 

V.    Ill;    VIII.     154;    X.    20'.   20), 

213,  214,  227  ;  xi.  235,  236,  241. 

246,  250 
Ecliptic,   obliquity  of,    i.    11  ;  n. 

35,  36,  42 ;  in.  59,  68 ;  iv.  83, 
,  84 ;  xi.  235,  236 
Ecole  Normale,  xi.  237,  238 
Ecole  Polytechnique,  xi.  237 
Egyptians,    Egyptian   astronomy, 

i.  6,   II,   12,   16;  n.  23,  26,  30, 

45 ;  iv.  75 
Elements  (of  Euclid),  in.  62,  66; 

ix.  165 
Elements  (of  an  orbit),  xi.  236, 

240,  242,  244,  246;  xm.   275, 

276 
Elements,     variation      of.        See 

Variation  of  elements 
Ellipse,  ii.  51  «  ;  in.  66  ;  vii.  140, 

141;  ix.  175,  176,  190,  194;  x. 

200,  209,  214;  xi.  228,  236,  242, 

244  ;  xm.  276,  278,  309 
Ellipticity,  x.  221 
Empty  month,  n.  19,  20 
Empyrean,  in.  68 
Enceladus,  xn.  255 
Encke's  comet,  xin.  291 
Encyclopaedia,  the  French,  xi.  232 
Energy,  xin.  319 
Ephemerides.     See  Almanacks 
Ephemerides  (of  Regiomontanus), 

in.  68 
Epicycle,  n.  37,  39,   41,    45,  48, 

51,  54;  in.  68;  iv.  85-87,  89- 

91;  vn.  139,  150;  viu.  163;  ix. 

170,  194 


Epitome  (of  Kepler),  vi.  132  ;  vn. 

144,  145 

Epitome  (of  Purbach),  in.  68 
Equant,  n.  51 ;  in.  62  ;  iv.  85,  89, 

91  ;  vii.  139,  150 
Equation  of  the  centre,  ii.  39,  48  ; 

in.  60;  v.  in 
Equator,  i.  9,  10,   II  ;  n.  33,  35, 

39,  42  ;  iv.  82,  84 ;  v.  98 ;  vi. 

129,  133  ;  ix.  187  ;  x.  207,  220, 

221 ;  xin.  285 

Equator,  motion  of.     See  Preces- 
sion 
Equinoctial  points,  i.  11,  13  ;  ii. 

42.    See  also  Aries,  first  point  of 
Equinoxes,  i.  11 ;  n.  39,  42 
Equinoxes,    precession    of.       See 

Precession 
Essai philosophique  (of  Laplace), 

xi.  238 

Ether,  xin.  293,  299 
Evection,  ii.  48,  52;  in.  60;  iv. 

85  ;  v.  1 1 1  ;  vii.  145 
Evening   star,    i.    14.      See    also 

Venus 
Exposition  du  Systeme  du  Monde 

(of  Laplace),  xi.  238,  242  n,  250 

Faculae,  vin.  153  ;   xin.  300,  301, 

3°3 
Figure  of  the  earth.     See  Earth, 

shape  of 

Firmament,  in.  68 
First  point  of  Aries,  Libia.     See 

Aries,  Libra,  first  point  of 
Fixed  stars,  i.  14.     See  Stars 
Fluxions,  ix.  169,  191  ;   x.  196 
Fluxions  (of  Maclaurin),  xii.  251 
Focus,  vii.  140,  141 ;  ix.  175;  xi. 

236 

Force,  vi.  130;  ix.  180,  181 
Fraunhofer  lines,  xm.  299,  300, 

3°3,  304 
Front-view      construction.       See 

Herschelian  telescopes 
Full  month,  ii.  19,  20 
Full  moon.     See  Moon,  phases  of 
Fundamenta  (of  Hansen),  xm.  286! 


43° 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Fundamenta  Astronomiae  (of 
Bessel),  x.  218;  xm.  277 

Funds  of  eccentricity,  inclination, 
xi.  245 

Galactic  circle,  xn.  258,  260 
Galaxy.     See  Milky  Way 
Gauges,      gauging.       See      Star- 
gauging 

Georgium  Sidus.     See  Uranus 

Gravitation,  gravity,  n.  38  n  ;  vn. 

150;  vin.  158,  161 ;  TX.. passim; 

x.   196,  201,  213,  215,  219,  220, 

223,  226 ;  XI.  passim  ;  xn.  264; 

xm.  282,  284,  286-293,  309,  3 1 9 

Gravitational  astronomy,  x.  196; 

xm.  272,  273,  286 
Gravity,   variation    of,   vm.   161 ; 
ix.  180;  x.  199,  217,  221,  223; 
xi.  231 

Great  Bear,  i.  12  ;  xn.  266 
Great  circle,  i.  11 ;  n.  33,  42 ;  iv. 

82,  84 

Gregorian   Calendar.      See    Cal- 
endar, Gregorian 
Grindstone  theory,  xn.  258 ;  xm. 
317 

Hakemite  Tables,  in.  60,  62 
Halley's  comet,  vn.   146  ;  x.  200, 
205;   xi.   231,   232;   xm.    291, 

307 

Harmonics  (of  Smith),  xn.  251 
Harmony  of  the  World (of  Kepler), 

vii.  144 

Heh'um,  xm.  301 
Herschelian    telescope,    xn.   255, 

256  ; 

Historia  Coelestis  (of  Flamsteed), 

x.  198 

Holy  Office.     See  Inquisition 
Horizon,  i.  3,  9;  ri.  29,  33,  35,  39, 

46;  vm.  161  ;  xm.  285 
Horoscopes,  v.  99 
Hour,  i.  1 6 

Hydrostatic  balance,  vi.  115  « 
Hyperbola,  ix.  190;  xi.  236  n 
Hyperion,  xm.  295 


Ilkhanic  Tables,  in.  62 

II  Saggiatore  (of  Galilei),  vi.  127 

Inclination,    in.    58;    iv.  89;    xi. 

228,  244,    245,  246,    250;  xm. 

294,  318 

Inclination  fund,  xi.  245 
Index  of  Prohibited  Books,  vi.  126, 

132;  vii.  145 
Indians,  Indian  astronomy,  i.  6 ; 

in.  56,  64 

Induction,  complete,  ix.  195 
Inequalities,  long,  xi.  243 
Inequalities,    periodic,    xi.    242, 

243,  245,  247 
Inequalities,     secular,     xi.     242, 

243-247  ;   xm.  282.      See  also 

Perturbations 

Inequality,  parallactic,  xm.  282 
Inferior  planets,  i.  15 ;  iv.  87,  88. 

See  also  Mercury,  Venus 
Inquisition  (Holy  Office),  vi.  126, 

13.2,  133 

Institute  of  France,  xi.  241 
Inverse  deductive  method,  ix.  195 
Inverse  square,  law  of,  ix.  172- 

176,  181,  195  ;  xi.  233.   See  also 

Gravitation 
Ionian  school,  n.  23 
Iris,  xm.  281 
Irradiation,  vi.  129 
Island  universe  theory,  xn.  260  ; 

xm.  317 

Japetus,  vm.  160;  xn.  267;  xm. 
297 

Julian  Calendar.  See  Calendar, 
Julian 

Juno,  xm.  294 

Jupiter,  i.  14-16;  n.  25,  51;  iv. 
81,  87,  88;  v.  98,  99;  vi.  121, 
127;  vii.  136  n,  142,  144,  145, 
150;  vm.  154,  156,  162;  ix. 
172,  181,  183,  185-187;  x.  204, 
216;  xi.  228,  231,  235,  236, 
243-245,  248  ;  xii.  267 ;  xm. 
281,  288,  294,  297,  305.  See 
also  the  following  headings 

Jupiter,  belts  of,  xii.  267 


General  Index 


43' 


{Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Jupiter,  mass  of,  ix.  183,  185 

Jupiter,  rotation  of,  vm.  160 ; 
ix.  187;  xm.  297 

Jupiter,  satellites  of,  n.  43  ;  vi. 
121,  127,  129,  133;  vn.  145, 
150;  vm.  1 60,  162;  ix.  170, 
184,  185  ;  x.  210,  216  ;  xi.  228, 
248 ;  xii.  267  ;  xm.  283,  295, 
297 

Jupiter's  satellites,  mass  of,  xi. 
248 

Kepler's  Laws,  vn.  141,  144,  145, 
151;  vm.  152;  ix.  169,  172, 
175,  176,  1 86,  194,  195  ;  x.  220; 
xi.  244 ;  xm.  294,  309 

Latitude    (celestial),   n.   33,    42, 

43 ;  in.  63  ;  iv.  89 
Latitude  (terrestrial),  m.  68,  69  ; 

iv.  73 ;  x.  221 ;  xm.  285 
Latitude,  variation  of,  xm.  285 
Law  of  gravitation.     See  Gravi- 
tation 
Laws   of  motion,  vi.    130,    133 ; 

vm.   152,   163;   ix.    171,    179- 

181,  183,  186,  194,  195  ;  xi.  232 
Leap-year,  i.  17;  n.  21,  22 
Least  squares,  xm.  275,  276 
Letter  to  the   Grand  Duchess  (of 

Galilei),  vi.  125 
Level  error,  x.  225  n 
Lexell's  comet,  xi.  248 ;  xm.  305 
Libra,  first  point  of  (^=),  1. 13 ;  n. 

42 
Librations  of  the  moon,  vi.  133  ; 

x.  226 ;  xi.  237,  239 
Libros  del  Saber,  m.  66 
Light-equation,  xm.  283 
Light,     motion    of,    velocity    of, 

vm.  162;  x.  208-211,  216,  220; 

xm.  278,  279,  283,   302.     See 

also  Aberration 
Logarithms,  v.  96,  97  n 
Long  inequalities,  xi.  243 
Longitude  (celestial),   n.  33,  39, 

42,  43 ;  m.  63  ;  iv.  87  ;  vn.  139 


Longitude    (terrestrial),    in.  68 ; 

vi.  127,  133;  vii.  150;  x.  197, 

216,  226 
Longitudes,      Bureau     des,     xi. 

238 

Lunar  distances,  m.  68  n 
Lunar  eclipses.     See  Eclipses 
Lunar  equation,  xm.  282 
Lunar  theory,  n.  48,  51  ;  v.  ill  ; 

vn.  145 ;  vm.  156  ;  ix.  184,  192  ; 

x.  226;  xi.  228,  230,  231,  233, 

234,  240,  241,  242,  248;  xm. 

282,  286,  287,  288,  290.      See 

also  Moon,  motion  of 
Lunation,  n.  40.    See  also  Month, 

synodic 

Macchie  Solari  (of  Galilei),  vi.  124, 

125 

Magellanic  clouds,  xm.  307 

Magnetism,  vn.  150;  xm.  276,  298 

Magnitudes  and  Distances  of  the 
Sun  and  Moon  (of  Aristarchus), 
n.  32 

Magnitudes  of  stars,  n.  42;  xn. 
266 ;  xn.  280,  316.  See  also 
Stars,  brightness  of 

Mars,  i.  14-16  ;  n.  25,  26,  30,  51  ; 
m.  68;  iv.  81,  87;  v.  108; 
vi.  129;  vii.  136  n,  139-142, 144, 
145 ;  vm.  154,  161  ;  ix.  181, 
183,  185  ;  x.  223,  227  ;  xi.  235, 
245  ;  xn.  267  ;  xm.  281,  282, 
284,  294,  295,  297.  See  also 
the  following  headings 

Mars,  canals  of,  xm.  297 

Mars,  mass  of,  xi.  248 

Mars,  opposition  of,  vm.  161;  xm. 
281,  284,  297 

Mars,  rotation  of,  vm.  160;  xm. 

295,  297 

Mars,  satellites  of,  xm.  295 

Mass,  ix.  180,  18 1,  185 

Mass  of  the  earth,  sun,  Venus  .... 
See  Earth,  Sun,  Venus ....  mass 
of 

Mecanique  Analytique  (of  La- 
grange),  xi.  237 


432 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles^ 


Mecanique    Celeste    (of    Laplace), 

xi.   238,   241,    247,    249,    250; 

xni.  292 
Medicean  Planets.     See  Jupiter, 

satellites  of 
Meraga,  in.  62 
Mercury,  i.  14-16  ;  n.  25,  26,  45, 

47,  51;  in.  66;  iv.  73,  75,  81, 

86-89;  vi.  121,  124;  vii.  136  n, 

139,  142,  144  ;  ix.  185  ;  xni.  288, 

290,    294,   297.      See  also  the 

following  headings 
Mercury,  mass  of,  xi.  248 
Mercury,  phases  of,  vi.  129 
Mercury,  rotation  of,  xm,  297 
Mercury,  transit  of,  x.  199 
Meridian,  n.  33,  39 ;  in.  57 ;  vi. 

127 ;  vm.  157  ;  x.  207,  218,  221 
Meteorologica  (of  Aristotle),  n.  27 
Meteors,  xm.  305 
Melon's  cycle,  n.  20 
Metric  system,  xi.  237 
Micrometer,  vm.   155 ;  xm.  279, 

,281 
Milky  Way,  n.   30,  33;  vi.  120; 

xn.  258,  260-262;  xm.  317 
Mimas,  xn.  255 
Minor    planets,   xi.    250  n ;    xm. 

276,  281,  284,  288,   294,    295, 

297,318 

Minor  planets,  mass  of,  xm.  294 
Minute  (angle),  i.  7 
Mira,  xn.  266 
Mongols,  Mongol  astronomy,  m. 

62 
Month,  i.  4,  1 6 ;  n.  19-21,  40,  48 ; 

ix.  173;  xi.  240;  xm.  293,  320. 

See  also  the  following  headings 
Month,  anomalistic,  11.  40 
Month,  draconitic,  11.  40,  43 
Month,  empty,  n.  19,  20 
Month,  full,  ii.  19,  20 
Month,  lunar,  i.  16;  11.  19,  20,  40 
Month,  sidereal,  n.  40 
Month,  synodic,  n.  40,  43 
Moon,  i.  I,  4,  5,    ii,   13-16;   ii. 

19-21,  25,  28,  30,  32,  39,  43 ; 

in.  68,  69 ;  iv.  81,  86 ;  v.  104, 


105  w;  vi.  119,   121,   123,  129, 

i3°>   J33J  vii.    145,    150;  vm. 

153;  ix.  169,  180,  181,  188,  189; 

x.  198,  204,  213,  215,  226;  xi 

228,  235  ;   xii.    256,  257,  271  ; 

xm.  272,   292,  293,  296,   297,, 

301,  320.    See  also  the  following' 

headings 
Moon,  aneular  or  apparent  size  of, 

n.  32,41,43,  46  n,  48;  iv.  73, 

85,  90  ;  v.  105  n 
Moon,  apparent  flattening  of,  ii. 

46 

Moon,  atmosphere  of,  xm.  296 
Moon,  distance  of,  i.   1 5  ;  n.  24, 

25,  30,32,41,43,  45>48,49,5i; 

iv.  85,  90 ;  v.  100,  103  ;  ix.  173 

185  ;  x.  223  ;  xm.  293,  320 
Moon,  eclipses  of.      See  Eclipses 
Moon,  librations  of,  vi.    133;   x. 

226;  xi.  237,  239 
Moon,    map    of,    x.     226 ;    xm. 

296 
Moon,   mass    of,    ix.    188,    189 

xi.  235 
Moon,  motion  of,  i.  4,  8,  13,  15, 

17  ;  ii.  20,   24-26,  28,  37,   39, 

40,  43,  47,  48,  51  ;  in.  60;  iv. 

73,  81,  85,  89,  90;  v.  in;  vi. 

133;  vii.   145.   150;  vm.   156; 

ix.  169,  173,  174,  179,  184,  185, 

189,  194,  195  ;  x.  201,  204,  213, 

226;  xi.  235,  237,  248 ;  xm.  287, 

290,  297,  320.     See  also  Lunar 

theory 

Moon,  origin  of,  xm.  320 
Moon,  parallax  of,  n.  43,  49  ;  iv. 

85.     Cf.  also  Moon,  distance  of 
Moon,  phases  of,  i.  4,   16,  17 ;  n. 

19,  20,  23,  28,  43,  48 ;  in.  68, 

69 ;  vi.  123 
Moon,  rotation  of,  x.  226 ;  xi.  248 ; 

xn.  267  ;  xm.  297 
Moon,   shape  of,   n.   23,  28,  46 ; 

vi.  119;  xi.  237 
Moon,  size  of,  ii.  32,  41  ;  iv.  85 
Moon,    tables    of.      See    Tables, 

lunar 


General  Index 


433 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.'} 


Moons.     See  Satellites 

Morning   star,    i.    14.      See  also 

Venus 

Morocco,  in.  6l 
Motion,    laws   of.     See  Laws   of 

motion 
Multiple  stars.     S^  Stars,  double 

and  multiple 

Mural  quadrant,  x.  218,  225  n 
Music  of  the  spheres,  11.  23  ;  vn. 

144 
Mysterium    Cosmographicum  (of 

Kepler),  v.  108;  vn.  136,  144 

Nadir,  in.  64 

Nautical  Almanac.    See  Almanac, 

Nautical 

Nebula  in  Argus,  xm.  307 
Nebula  in    Orion,  xn.    252,  259, 

260;  xm.  311 

Nebulae,    x.   223 ;    xi.  250 ;   xn. 
.       252  256,   259-261 ;  xm.  306- 

308,  310,  311,  317,  318,  319,  320 
Nebulae,  spiral,  xm.  310 
Nebular  hypothesis,  xi.  250;  xm. 

318-320 
Nebulous  stars,  x.  223  ;  xn.  260, 

261 

Neptune,  xm.  289,  295,  297 
Neptune,  satellite  of,  xm.  295 
New  Almagest  (of  Kepler),  vn 

148 
New  Almagest  (of  Riccioli),  vni. 

J53 

New  moon.     See  Moon,  phases  of 
New  stars.     See  Stars,  new 
New  Style   (N.S.),   n.   22.     See 

also  Calendar,  Gregorian 
Newton's  problem,  xi.  228,  229, 

249 
Newtonian    telescope,    ix.    168; 

xn.  252,  253,  256 
Night-hour,  i.  16 
Node,  n.  40,  43;  v.  in  ;  ix.  184  ; 

x.  213,  214;  xi.  236,  246 
Nubeculae,  xm.  307 
Nucleus  (of  a  comet),  xm.  304 
Niirnberg  school,  in.  68  ;  iv.  73 


Nutation,  x.   206,    207,   213-215, 
216,  218  ;  xi.  232,  248  ;  xn.  263 
',  i.  l6« 


Oberon,  xn.  255 

Obliquity   of    the   ecliptic.      See 

Ecliptic,  obliquity  of 
Observational     astronomy,     xm. 

272,  273 

Occultations,  i.  15  ;  n.  30 
Octaeteris,  11.  19 
Olbers's  comet,  xm.  291 
Old  Moore's  Almanack,  i.  18  n 
Old  Style  (O.S.).     See  Calendar, 

Julian 
Opposition,  n.  43,  48  n  ;  m.  60  ; 

iv.  87,  88;  v.  in  ;  vm.  161  ; 

xm.  281,  284,  297 
Opposition   of   Mars,   vm.    161  ; 

xm.  281,  284,  297 
Optical  double  stars,  xn.  264 
Optics  (of  Gregory),  x.  2O2 
Optics  (of  Newton),  ix.  192 
Optics  (of  Ptolemy),  n.  46 
Optics  (of  Smith),  xn.  251 
Opus    Majus,     Minus,     Tertium 

(of  Bacon),  in.  67 
Opuscules      Mathe'matiques      (of 

D'Alembert),  xi.  233 
Orion,   nebula  in,   xii.  252,  259, 

260;  xm.  311 
Oscillatorium     Horologium      (of 

Huygens),  vm.  158  ;  ix.  171 

Pallas,  xm.  294 

Parabola,    ix.    190  ;    xi.    236  n  ; 

xm.  276 

Parallactic  inequality,  xm.  282 
Parallax,  n.  43,  49;  iv.  85,   92; 

v.  98,  100,  no;  vi.  129;  vn. 

145;   vm.   161;    x.   207,   212, 

223,  227;  xn.   257,   258,   263, 

264  ;  xm.  272,  278,   279,  281- 

284 
Parallax,  annual,   vm.   161.     See 

also  Parallax,  stellar 
Parallax,  horizontal,  vm.  161 


434 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Parallax  of  the  moon.    See  Moon, 

parallax  of 
Parallax   of  the   sun.     See   Sun, 

parallax  of 
Parallax,  stellar,  iv.  92;  v.  100 ; 

vi.  129  ;  vin.  161 ;  x.  207,  212  ; 

xii.  257,  258,  263,  264;    xni. 

272,  278,  279 

Parallelogram  offerees,  ix.  i8o« 
Parameters,  variation  of,xi.233  n. 

See  also  Variation  of  elements 
Hapatrriy/AaTa,  n.  2O 
Partial  eclipses,  n.  43 
Pendulum,     pendulum   clock,    v. 

98;    vi.   114;    vm.   157,    158, 

161;  ix.  180,  187  ;  x.  199,  217, 

221,   223;    xi.   231.      See  also 

Gravity,  variation  of 
Pendulum   Clock   (of  Huygens), 

vm.  158;  ix.  171 
Penumbra   (of    a   sun-spot),   vi. 

124 ;  xii.  268 
Perigee,  n.   39,  40,   48;    iv.    85. 

See  also  Apse,  apse-line 
Perihelion,  iv.  85  ;  xi.  231.     See 

also  Apse,  apse-line 
Periodic    inequalities.       See    In- 
equalities, periodic 
Perturbations,  vm.  156;  ix.  183, 

184 ;  x.  200,  204,  224,  227  ;  XI. 

passim  ;  xm.  282,  293,  294,  297 
Phases  of  the  moon.     See  Moon, 

phases  of 

Phenomena  (of  Euclid),  n.  33 
Phobos,  xm.  295 
Photography,  xm.  274,  279-281, 

294,  298,  299,  301,  306 
Photometry,  xm.  316.     See  also 

Stars,  brightness  of 
Photosphere,  xii.  268  ;  xm.  303 
Physical  double   stars,  xii.  264. 

See  also  Stars,  double  and  mul- 
tiple 
Planetary    tables.      See    Tables, 

planetary 
Planetary  theory,  n.  51,  52,  54; 

m.  68  ;  iv.  86-90  ;  xi.  228,  230, 

231,   233,   235,   236,    242-247, 


248;  xm.  286,  288-290,  293. 
See  also  Planets,  motion  of 
Planets,  i.  13,  14,  15,  16;  n.  23- 
27,  3°»  32>  5i  J  m-  68;  iv.  81; 
v.  104,  105,  no,  112;  vi.  119, 
121  ;  vn.  136,  144;  vm.  154, 
155;  x.  200;  xi.  228,  250;  xii 

253,  255,   257,  267,  271;  xm. 
272,   275,  276,  281,  282,  294- 
296,  297,   318,    320.      See  also 
the  following  headings,  and  the 
several  planets  Mercury,  Venus, 
etc. 

Planets,  discoveries  of,  xii.  253, 

254,  255,  267;  xm.  289,  294, 
295,318 

Planets,  distances  of,  i.  15  ;  n.  30, 
51  ;  iv.  81,  86,  87;  vi.  117; 
vn.  136,  144;  ix.  169,  172,  173 

Planets,  inferior,  i.  15  ;  iv.  87,  88. 
See  also  Mercury,  Venus 

Planets,  masses  of,  ix.  185 ;  xi. 
245,  248;  xm.  294.  See  also 
under  the  several  planets 

Planets,  minor.  See  Minor  planets 

Planets,  motion  of,  i.  13,  14,  15; 
ii.  23-25,  26,  27,  30,  41,  45,  47, 
51,  52 ;  m.  62,  68 ;  iv.  81,  86- 
90,  92;  v.  loo,  104,  105,  112; 
vi.  119,  121,  129;  vn.  139-142, 
144,  145,  150,  151;  vm.  152, 
156;  ix.  169, 170, 172-177,  181, 
183,  194;  x.  199,  204;  xi.  228, 
229,  245,  250;  xm.  275,  276, 
282,  294.  See  also  Planetary 
theory 

Planets,  rotation  of,  vm.  160;  ix. 
187;  xi.  228,  250;  xii.  267; 
xm.  297 

Planets,  satellites  of.  See 
Satellites 

Planets,  stationary  points  of,  i. 
14;  11.51;  iv.  88 

Planets,  superior,  1. 15 ;  iv.  87,  88. 
See  also  Mars,  Jupiter,  etc. 

Pleiades,  vi.  120;  xii.  260 

Poles  (of  a  great  circle),  n. 
33  » 


General  Indjx 


435 


\Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles .] 


Poles  (of  the  celestial  sphere),  i. 

8,  9,  10 ;  ii.  33,  35 ;  iv.  78  ;  vi. 

129;  x.  207,  214;  xni.  285 
Poles  (of  the  earth),  iv.  82  ;  ix. 

187;  x.  220,  221  ;  xin.  285 
Pole-star,  i.  8,  9 
Pollux,  xu.  266 
Pons-Brooks  comet,  xni.  291 
Postulates  (of  Ptolemy),  n.  47 
Postulates   (of  Coppernicus),  iv. 

76 

Praesepe,  xn.  260 
Precession    (of    the   equinoxes), 

n.  42,  50 ;  in.  58,  59,  62,  68  ; 

iv.  73.  83»  84  85;  v.  104,  112; 

vi.  129;  ix.  188,  192;  x.  213- 

215,   218,    221  ;  xi.   228,   232, 

248;  xni.  277,  280 
Prima   Narratio    (of  Rheticus), 

iv.  74 ;  v.  94 
Primum  Mobile,  in.  68 
Principia  (of  Descartes),  vin.  163 
Princlpia  (of  Newton),  iv.  75  J  vni. 

152;  ix.  164,  177-192,  195  ;  x. 

196,  199,  200,  213;  xi.  229,  234, 

235.  240 
Principles      of     Philosophy      (of 

Descartes),  vni.  163 
Probabilite's,    The'orie    Analytique 

des  (of  Laplact),  xi.  238 
Problem    of   three   bodies.      Sec 

Three  bodies,  problem  of 
Prodrontus  Cometicus  (of  Revel), 

vni.  153 

Prominences,  xni.  301,  302,  303 
Proper  motion  (of  stars),  x.  203, 

225  ;  xii.  257,  265  ;  xin.  278,  280 
Prosneusis,  n.  48;  in.  60 ;  iv.  85 
Prussian  'Lables,  v.  94,  96,  97, 

99J  vii.  139 
Pythagoreans,  11.  24 ;    iv.  75 

Quadrant,  v.  99  ;  x.  218,  225  ;/ 
Quadrature,  n.  48;  in.  60;  v.  in 
Quadruium,  in.  65 

R-cherches  sur  differ  ens  points  (of 
D'Alembert),  xi.  233,  235 


Recherches   sur   la  precession    (of 

D'Alembert),  xi.  215 
Reduction     of    observation?,     x. 

198,  218;   xm.  277 
Reflecting    telescopes,    ix.    168  ; 

xii.  251-255 
Refracting    telescopes,    ix.     1 68. 

See  a.'so  Telescopes 
Refraction.  11.  46  ;   in.  68  ;  v.  98, 

110  :  vn.  138;   vni    159,  160; 

x.  217,  218,  223;  xin  277 
Relative    motion,     principle     of, 

iv.  77 ;  ix.  186  n 
Renaissance,  iv.  70 
Results  of  Astronomical  Observa- 
tions (of  John  Herschel),  xin. 

308 

Retrograde  motion,  i.  14 
Reversing  stratum,  xin.  303 
Reviews  of  the  heavens,  xii.  252, 

253 

Revival  of  Learning,  iv.  70 
Rnta,  vni.  160 
Rigel,  in.  64 
Right   ascension,   n.    33,   39;   x. 

198,  218;  xm.  276 
Rills,  xni.  296 
Rings   of  Saturn.      See   Saturn, 

rings  of 
Rotation  of  the  celestial  sphere. 

See  Daily  motion 
Rotation  of  the  earth,  sun,  Mars, 

etc.      See    Earth,    Sun,    Mars, 

etc.,  rotation  of 
Royal  Astronomical  Society.    See 

Astronomical  Society,  Royal 
Royal  Society,  ix.  1 66,  174,   177, 

191,  192  ;  x.  201,  202,  206,  208  ; 

xii.   254,    256,  259,   263;   xm. 

292,  308 
Rudolphine    Tables,    v.    94 ;   vii 

148,  151  ;  vni.  156 
Ruler,  i.  16 
Running     down     of     the     solar 

system,  xm.  293,  319 

Saggiaiore  (of  Galilei),  vi.  127 
Sappho,  xm.  281 


436 


General  Index 


[Roman  figures  refer  to  the  chapters  Arabic  to  the  articles.] 


Saros,  i.  17  ;  n.  43 

Satellites,  vi.  121,  127,  129,  133  ; 

vn.    145,    150;   vni.  154,   160, 

162;  ix.  170,  183-185;  x.  210, 

216;   xi.    228,   248;  xn.    253, 

255,  267;  xm.   272,   283,  295, 

296,    297,  318,   320.     See  also 

Jupiter,  Saturn,  etc.,  satellites 

of 
Satellites,  direction  of  revolution 

of,  xi.  250;  xm.  295,  318 
Satellites,    rotation    of,    xi.    250 ; 

xn.  267  ;  xm.  297 
Saturn,  i.    14-16;  n.  25,  51;  iv. 

81,    87;   v.   99;   vi.    123;   vn. 

136  n,  142,  144;  vin.  154,  156; 

ix.   183,  185,   186;  x.  204;  xi. 

228,   231,   235,   236,   243-246; 

xn.  253,  267;  xni.    288,  297. 

See  also  the  following  headings 
Saturn,  mass  of,  ix.  185 
Saturn,    rings   of,    vi.    123 ;  vin. 

154,  160 ;  xi.  228,  248 ;  xn.  267; 

xm.  295,  297 
Saturn,  rotation  of,  xn.  267  ;  xm. 

297 

Saturn,  satellites  of,  vin.  154, 
160  ;  ix.  184  ;  xi.  228  ;  xn.  253, 
255,  267 ;  xni.  295,  297,  307 

Scientific  method,  n.  54  ;  vi.  134  ; 
ix.  195 

Seas  (on  the  moon),  vi.  119;  vin. 
153;  xm.  296 

Seasons,  i.  3  ;  n.  35,  39  ;  iv.  82 ; 
xi.  245 

Second  (angle),  i.  7 

Secular  acceleration  of  the  moon's 
mean  motion,  x.  201  ;  xi.  233, 
234,  240,  242  ;  xni.  287 

Secular  inequalities.  See  In- 
equalities, secular 

Selenographia     (of    Hevel),   vin. 

*53 

Selenotopographische      Fragmente 

(of  Schroeter),  xn.  271 
Sequences,  method  of,  xn.  266 
Shadow    of   earth,    moon.      See 
Eclipses 


"  Shining-fluid  "  theory,  xn.  260; 

xm.  310,311 

Shooting  stars.     See  Meteors 
Short-period  comets,  xm.  291 
Sidereal  month,  n.  40 
Sidereal  period,  iv.  86,  87 
Sidereal  system,  structure  of,  xn. 

257,  258,  259-262;  xm.  317 
Sidereal  year,  n.  42 
Sidereus  Nuncius  (of  Galilei),  vi. 

119-122 
"Sights,"  v.    no;  vm.    155    x. 

198 

Signs  of  the  zodiac,  i.  13 
Sine,  ii.  47  n  ;  in.  59  n,  68  n 
Sirius,  xm.  316  n 
Solar  eclipse.     See  Eclipse 
Solar  system,  stability  of,  xi.  245  ; 

xm.  288,  293 

Solstice?,  i.  11 ;  n.  36,  39,  42 
Solstitial  points,  i.  1 1 
Space- penetrating      power,     xn. 

258 

Spanish  astronomy,  in.  6 1,  66 
Spectroscope,  xm.  299.     See  also 

Spectrum  analysis 
Spectrum,  spectrum  analysis,  ix. 

1 68;  xm.    273,  299-302,    303, 

304,306,309,311-314,317,318 
Sphacra  Mundi  (of  Sacrobosco), 

in.  67 

Sphere,    attraction    of,    ix.     173, 
.    182 ;  xi.  228 
Sphere,    celestial.     See   Celestial 

sphere  . 
Sphere,    doctrine    of    the.      See 

Spherics 
Spheres,   celestial,   crystal.      Sec 

Celestial  spheres 
Spheres,  music  of  the,  n.  23 ;  vn. 

144 
Spherical  form  of  the  earth,  moon. 

See  Earth,  Moon,  shape  of 
Spherics,  n.  33,  34 
Spica,  ii.  42 

Spiral  nebulae,  xm.  310 
Stability  of  the  solar  system,  xi. 

245  ;  xm.  288,  293 


General  Index 


437 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles] 


Stadium,  n.  36,  45,  47 

Star-atlases,  star-maps,  i.  12  w; 
x.  198,  223 ;  xn.  259,  266;  xni. 
280,  294 

Star-catalogues,  n.  32,  42,  50; 
in.  62,  63 ;  iv.  83 ;  v.  98,  107, 
1 10,  112;  vin.  153  ;  x.  198, 199, 
205,  218,  223-225 ;  xn.  257 ; 
xin.  277,  280,  316 

Star-clusters,  vi.    I2O;    x.    223; 
xn.  258,  259,   260,   261  ;  xni. 
307,  308,  310,  311,  318 
•  Star-gauging,  xn.  258;  xni.  307 

Star-groups.     See  Constellations 

Stars,  i.  I,  5,  7-10,  12-15,  J8;  n. 
20,  23-26,  29,  30,  32,  33,  39,  40, 
42,  45-47,  50;  m.  56,  57,  62, 
68 ;  iv.  73,  78,  80,  86,  89,  92  ; 
v.  96-100,  104,  105,  no;  vi.  120, 
121,  129;  vin.  155,  157,  161  ; 
ix.  1 86  n  ;  x.  198,  199,  203,  207- 
214,  218,  223  ;  xi.  228 ;  xii.  253, 
257-266,  267  ;  xni.  272,  277- 
280,  283,  304,  306-318,  320. 
See  also  the  preceding  and  fol- 
lowing headings 

Stars,  binary.  See  Stars,  double 
and  multiple 

Stars,  brightness  of,  n.  42  ;  xn. 
258,  266;  xin.  278,  280,  316, 
317.  See  also  Stars,  variable 

Stars,  circumpolar,  i.  9 ;  n.  35 

Stars,   colours  of,  xn.  263  ;  xin. 

309 
Stars,  distances  of,  i.  7  ;  n.  30,  32, 

45>  47  >  IV-  80,  92 ;  v.  100 ;  vi. 

117,   129;    xi.  228;    xii.   257, 

258,  265,  266  ;  xin.   278,  279, 

317.     See  also  Parallax,  stellar 
Stars,   distribution    of,    xn.    257, 

258.    See  also  Sidereal  system, 

structure  of 
Star?,  double  and    multiple,  xn. 

256,  263,  264;    xni.   306-308, 

3o9,  314,  320 
Stars,  magnitudes  of,  n.  42 ;  xn. 

266  ;   xin.  280,  316.     See  also 

Stars,  brightness  of 


Stars,     motion     of.      See    Stars, 

proper   motion   of,   and  Daily 

motion  (of  the  celestial  sphere) 
Stars,  names  of,  i.  12,  13  ;  in.  64 
Stars,  nebulous,  x.  223  ;  xn.  260, 

261 
Stars,  new,  n.  42  ;  v.  100,   104 ; 

vi.  117,  1 29;  vn.  1 38;  xii.  266; 

xm.  312 

Stars,  number  of,  i.  7  n  ;  xin.  280 
Stars,  parallax  of.     See  Parallax, 

stellar 
Stars,  proper  motion  of,  x.  203, 

225  ;  xii.    257,  265 ;  xm.  278, 

280 

Stars,  rotation  of,  xii.  266 
Stars,  spectra  of,   xm.  311-314, 

3*7 

Stars,  system  of.  See  Sidereal 
system,  structure  of 

Stars,  variable,  xii.  266,  269; 
xm.  307,  312,  314,  315 

Stationary  points,  i.  14;  11.  51  ; 
iv.  88 

Stjerneborg,  v.  101 

Summer  solstice,  i.  n.  See  also 
Solstices 

Sun,  i.  i,  4,  10,  13,  14,  16;  11.  21, 
23-26,  28-30,  32,  35,  36,  40, 
43.  45,  48,  51  ?  "I-  68>  69;  iv. 
73,  75,  77,  79-82,  85-90,  92 ; 
v.  98,  103,  105,  no,  in;  vi. 
119,  121,  123,  124,  126,  127, 
129,  132;  vn.  136,  139-141, 
144-146,  150;  vin.  153,  154, 
156;  ix.  170,  172-1751  l8l» 
183-186,  188-190,  194;  x.  198, 

200,    202,    205,    210,    213,    223, 

227 ;  xi.  228,  235,  236,  240,  243, 

245,2505x11.257,265,268,269; 

xm.  272,  278,  283,  288,  292- 
294,  297,  298-303,  304,  305, 
307,  319,  320.  See  also  the 
following  headings 

Sun,  angular  or  apparent  size 
of,  n.  32,  38,  39,  41,  43,  46  n, 
48 ;  iv.  73,  90 ;  v.  105  n 

Sun,  apparent  flattening  of,  n.  46 


General  Index 


[Roman  figures  refer  to  the  chapters,  Arabic  to  the  articles.'] 


Sun,  distance  of,  i.  15  ;  n.  24,  25, 

30,32,38,41,43,45,48,49,51; 

iv.  8 1,  85,   86,  87,  90,  92;  v. 

in;  vu.    144,    145;   vin.   156, 

161;  ix.  185,  188;  x.  202,  205, 

223,  227  ;  xi.    235  ;    xm.    278, 

281-284 

Sun,  eclipses  of.     See  Eclipses 
Sun,  heat  of,  xn.  268,  269 ;  xm. 

303,  307,  319 
Sun,  mass  of,   ix.  183,    184,  185, 

189;  xi.  2^8;  xm.  282 
Sun,  motion  of,  i.   3,  5,  8,  10,  11, 

13,  15-17;  ii.  20,21,  24-26,  35, 

37,88,39,40,42,43,47,48,51; 

in.  59 ;  iv.  73,  77,  79,  85,  86,  87, 

92;  v.  104,  105,    in;  vi.    121, 

126,    127,    132;   vin.    1 60;    ix. 

186 ;  x.  223  ;  xi.  235  ;  xn.  265  ; 

xm.  288 
Sun,    parallax   of,  11.  43  ;  v.  98, 

1 10  ;  vu.  145  ;  VIH.  161 ;  x.  223, 

227;   xm.    281-284.     See  also 

Sun,  distance  of 
Sun,  rotation    of,    vi.    124;    vu. 

150 ;  xi.  250  ;  xm.  297,  298,  302 
Sun,  size  of,  n.  32 ;  iv.  85  ;  vu. 

145;  ix.  173;  xm.  319 
Sun,  tables  of.     See  Tables,  solar 
Sun-dials,  n.  34 
Sun-spots,  vi.  124,  125;  vin.  153; 

xii.  268,    269;  xm-  298,  300, 

3°2,  303 
Superior  planets,  i.   15  ;    iv.  87, 

88.   See  also  Mars,  Jupiter,  etc. 
Svea,  xm.  294 
Synodic  month,  n.  40,  43 
Synodic  period,  iv.  86,  87 
Synopsis  of  Cometary  Astronomy 

(of  Halley),  x.  200 
Systema  Saturnium  (of  Huygens), 
.  Yin.  154 
Systeme  du  Monde  (of  Laplace), 

xi.  238,  242  n,  250 
Systeme    du    Monde   (of    Ponte- 

coulant),  xm.  286 

Table  Talk  (of  Luther),  iv.  73 


Tables,  astronomical,  in.  58,  60  - 

63,  66,  68 ;  iv.  70 ;  v.  94,  96, 

97,  99,  no;  vn.  139,148;  vin. 

156,  160;  x.  216,  2^17;  xm.  277. 

See  also  the  following  headings 
Tables,  lunar,  n.  48;  in.  59;  x. 

204,  216,  217,  226 ;  xi.  233,  234, 

241  ;  xm.  286,  290 
Tables,  planetaiy,  in.  63 ;  v.  108, 

1 12;  vii.  142,  143;  x.  204,  216; 

xi.  235,  247;  xm.  288,  289,  290 
Tables,    solar,    in.    59 ;    iv.    85 ; 

v.  in  ;  vin.  153  ;  x.  224,  225^ 

226 ;  xi.  235,  247  ;  xm.  290 
Tables,    Alfonsine,    in.    66,    68; 

v.  94,  96,  99 

Tables,  Hakemite,  in.  60,  62 
Tables,  Ilkhanic.  in.  62 
Tables,   Prussian,  v.  94,  96,  97, 

99;  vii.  139 
Tables,    Rudolphine,  v.    94;  vii. 

148,  151  ;  vin.  156 
Tables,  Toletan,  in.  61,  66 
Tables  delaLune  (of  Damoiseau^, 

xm.  286 
Tabulae  Regiomontanae  (of  Bes- 

sel),  xm.  277 
Tangent,  in.  59  «,  68  n 
Tartars,  Tartar  astronomy,  111.63 
Tebbutt's  comet,  xm.  305 
Telescope,   in.  67 ;  vi.    118-124, 

134;  vii.  138;    vm.  152-155; 

ix.  168;  x.  207,  213,  218;  xn. 

251,   252-258,    260,    262,  271; 

xm.  274,   300,   301,   306,  310, 

3»7 
Theoria   Motus  (of  Gauss),   xm. 

276 
Theoria  MotuumLunae(ofEu\er}, 

xi   233 
The'orie  de  la  Lune  (of  Clairaut), 

xi.  233 
Theorie  .  .  .  des  Probabilites  (of 

Laplace),  xi.  238 
Theorie  .  .  .  du  Systeme  du  Monde 

(of  Pontecculant),  xm.  286 
Theory  of  the  Moon    (of  Mayer), 

x.  226 


General  Index 


439 


\Romanfigures  refer  to  the  chapters,  Arabic  to  the  articles.] 


Theory  of  the  Universe  (of  Wright), 

xn.  258 

Thetis,  viii.  160 
Three  bodies,  problem  of,  xi.  228, 

230-233,  235 
Tidal  friction,  xm.  287,  292,  293, 

320 
Tides,  vi.  130;  vn.  150;  ix.  189; 

xi.  228-230,  235,  248 ;  xm.  287, 

292,  293,  297,  320 
Time,  measurement  of,  i.  4,  5,  16. 

See  also  Calendar,  Day,  Hour, 

Month,  Week,  Year 
Titan,  vm.  154    • 
Titania,  xn.  255 
Toletan  Tables,  HI.  61,  66 
Torrid  zones,  H.  35 
Total   eclipse,    n.   43 ;  VH.    145 ; 

x.    205 ;    xm.    301.      See  also 

Eclipses 

Transit  instrument,  x.  218,  225  n 
Transit  of  Mercury,  x.  199 
Transit   of  Venus,  vm.  156;    x. 

202,   205,   224,  227;  xm.  281, 

282,  284 
Translations,  HI.  56,   58,  60,  62, 

66,  68 

Transversals,  v.  110  n 
Trepidation,  HI.    58,  62,  68 ;  iv. 

84;  v.  112 
Trigonometry,  n.  37  n,  47  n ;  HI. 

59  n,  64  n,  68  n ;  iv.  74 
Trivium,  HI.  65 
Tropical  year,  n.  42 
Tuttle's  comet,  xm.  291 
Twilight,  in.  69 
Twinkling  of  stars,  n.  30 
Two  New  Sciences   (of   Galilei), 

vi.  133,  134**;  vm.  152 
Tyohonic  system,  v.  105;  vi.  127 

Umbra    (of  sun-spots),  vi.  124; 

xn.  268 
Uniform     acceleration,    vi.     133. 

See  also  Acceleration 
Uraniborg,  v.  IOI 
Uranotnetria    Nova     Oxoniensis, 

xin.  316 


Uranus,  xn.  253,  254,  255,  267  ; 

xin.  276,  288,  289,  297 
Uranus,  rotation  of,  xm.  297 
Uranus,  satellites    of,  xi.    250  n  ; 

xn.  255,  267  ;  xm.  272,  295 

Variable  stars.  See  Stars,  vari- 
able 

Variation  (of  the  moon),  m.  60 ; 
v.  Ill ;  VH.  145 

Variation  of  elements  or  para- 
meters, xi.  233  n,  236,  245 

Variations,  calculus  of,  xi.  237  n 

Vega,  in.  64 

Venus,  i.  14-16;  n.  25,  26,  45, 
47,  51;  HI.  68;  iv.  75,  8:,  86, 
87;  v.  98,  100,  103;  vi.  121, 
123;  vii.  136  »,  139,  142,  144; 
vm.  154;  ix.  181,  185;  x.  223, 
227;  xi.  235,  245;  xn.  267, 
271;  xin.  282,  297.  See  also 
the  following  headings 

Venus,  mass  of,  xi.  235,  248 

Venus,  phases  of,  vi.  123,  129 

Venus,  rotation  of,  vm.  160;  xn. 
267  ;  xm.  297 

Venus,  transits  of.  See  Transits 
of  Venus 

Vernal  equinox,  i.  n.  See  also 
Equinoxes 

Vernier,  in.  69  n 

Vertical,  n.  33;  x.  221 ;  xm. 
285 

Vesta,  xm.  294 

Victoria,  xm.  281 

Virtual  velocities,  xi.  237  n 

Vortices,  vm.  163;  ix.  178, 
195 

Wave,  wave-length  (of  light) 
xin.  299,  300,  302 

Weather,  prediction  of,  n.  2O 
VH.  136 

Week,  i.  1 6 

Weight,  vi.  116,  130;  ix.  180 

Weights  and  Measures,  Com- 
mission on,  xi.  237,  238 


440 


General 


[Roman  figures  rejer  to  the  chapters,  Arabic  to  the  articles.'] 


Whetstone  of  Witte  (of  Recorde), 

v.  95 

Winter  solstice,  i.  n.     See  also 
Solstices 

Year,  i.  3,  4,   16 ;  11.   19-22,    42, 

47 ;  in.  66 ;  v.  1 1 1 
Year,  sidereal,  n.  42 
Year,  tropical,  11.  42 


ZadkieVs  Almanack,  i.  18  n 
Zenith,  n.  33,  35,  36,  46 ;  in.  64  , 

x.  221 

Zenith-sector,  x.  206 
Zodiac,  i.  13  ;  x.  224 
Zodiac,  signs  of  the,  i.  13 
Zodiacal  constellations,  i.  13 
Zones  of  the  earth,  n.  35,  47 


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